Tuesday, December 5, 2023

# Algebra Break Even Word Problems

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Word Problems III: Break Even

If reading is a struggle, read the word problems out loud. This simple change can help kids keep learning math even if reading is a challenge.

Word problems in math can be tricky. To get the right answer, kids have to be able to read the words, figure out what math operation to use, and then do the calculations correctly. A breakdown in any of these skills can cause trouble.

If kids seem to be good at math but struggle with word problems, here are possible reasons why:

Trouble with reading: To solve word problems, kids have to read well. So even if they usually do well with math, reading difficulties can make word problems hard.

Trouble understanding math phrases and concepts: Even if kids are strong readers, they may have trouble picking up on clues in word problems. These clues are phrases that help kids figure out what they need to do to solve the problem, like adding or subtracting. Kids then have to translate these phrases into a number sentence, like two plus three equals five.

Trouble with focus and self-control: Kids may get distracted by the words or get lost in their heads. Other kids struggle with self-control and rush through the problem. They may skip important parts or make simple calculation mistakes.

Patience and Practice are the two key points of focus!

Maths word problems are difficult for children to solve because they require the ability to analyse data and extract only the relevant information. Instead of being told what operation they need to perform, they must figure it out for themselves before they can begin to solve the problem. As a result, children frequently struggle to solve word problems correctly, leading to frustration and dissatisfaction with their work.

## Translate The Problem Into Equations With Variables

First, we need to translate the word problem into equation with variables. Then, we need to solve the equation to find the solution to the word problems.

How to recognize some common types of algebra word problems and how to solve them step by step.

The following shows how to approach the common types of algebra word problems.

Age Problems usually compare the ages of people. They may involve a single person, comparing his/her age in the past, present or future.

Average Problems involve the computations for arithmetic mean orweighted average of different quantities.Another common type of average problems is the average speed computation.

Coin Problems deal with items with denominated values.

Consecutive Integer Problems deal with consecutive numbers.The number sequences may be Even or Odd, or some other simple number sequences.

Digit Problems involve the relationship and manipulation of digits in numbers.

Distance Problems involve the distance an object travels at a rate over a period of time.We can have objects that Travel at Different Rates, objects thatTravel in Different Directions or we may need to find the distanceGiven the Total Time

Fraction Problems involve fractions or parts of a whole.

Geometry Word Problems deal with geometric figures and angles described in words.This include geometry word problems Involving Perimeters,Involving Areas andInvolving Angles

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## What Is A Break Even Analysis

The idea of breaking even in real life is that I don’t lose or win either. And that is exactly the idea behind break-even analysis: you need determine how many units you need to produce so that your profit is 0, so don’t lose or win, you just break-even.

So, the break even point corresponds to the number of units you need to sell in order to break even. If you sell less than that, you make a loss, and if you sell more than that, you make a profit.

## Example: Alex Puts $2000 In The Bank At An Annual Compound Interestof 11% How Much Will It Be Worth In 3 Years This is the compound interest formula: So we will use these letters: • Present Value PV =$2,000

Note: we could have also tried “guess and check”:

• We could try, say, n=10: 10 = 120 NO
• Next we could try n=12: 12 = 168 YES

But unless we remember that multiplying two negatives make a positive we might overlook the other solution of ×.

And:

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## How To Solve Word Problems In Algebra

This article was co-authored by Daron Cam. Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary’s College. This article has been viewed 40,135 times.

You can solve many real world problems with the help of math. In order to familiarize students with these kinds of problems, teachers include word problems in their math curriculum. However, word problems can present a real challenge if you don’t know how to break them down and find the numbers underneath the story. Solving word problems is an art of transforming the words and sentences into mathematical expressions and then applying conventional algebraic techniques to solve the problem.

## Using Systems Of Equations To Investigate Profits

Using what we have learned about systems of equations, we can return to the skateboard manufacturing problem at the beginning of the section. The skateboard manufacturers revenue function is the function used to calculate the amount of money that comes into the business. It can be represented by the equation R=xp, where x= quantity and p= price. The revenue function is shown in orange in Figure 10.

The cost function is the function used to calculate the costs of doing business. It includes fixed costs, such as rent and salaries, and variable costs, such as utilities. The cost function is shown in blue in Figure 10. The x -axis represents quantity in hundreds of units. The y-axis represents either cost or revenue in hundreds of dollars.

The point at which the two lines intersect is called the break-even point. We can see from the graph that if 700 units are produced, the cost is $3,300 and the revenue is also$3,300. In other words, the company breaks even if they produce and sell 700 units. They neither make money nor lose money.

The shaded region to the right of the break-even point represents quantities for which the company makes a profit. The shaded region to the left represents quantities for which the company suffers a loss. The profit function is the revenue function minus the cost function, written as P\left=R\left-C\left. Clearly, knowing the quantity for which the cost equals the revenue is of great importance to businesses.

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## Algebra Word Problems Worksheets

In algebra word problems worksheets, we will talk about algebra, which is a branch of mathematics dealing with symbols and the rules for manipulating these symbols. They represent quantities without fixed values, known as variables. Solving algebraic word problems requires us to combine our ability to create and solve equations. Translating verbal descriptions into algebraic expressions is an essential initial step in solving word problems.

## Word Problem Wednesday: Grocery Budget Math

Using Linear Equations to Solve Word Problems – Break Even Point

What do you like to buy when you go to the store? When youre shopping on a budget you have to think carefully about what youre going to put in your cart. Are you a cookies and milk person? Do you prefer ice-cream? Or are you more likely to want apples and peanut butter? In this weeks word problem challenge you can practice your elementary school math skills such as multiplication, addition, subtraction, and money math to help Eric figure out how much he has to spend on groceries if he buys the sweets he wants.Question: Eric has $31.00 to spend on groceries. He has 4 boxes of cookies that cost$2.85 each and a half-gallon of milk that costs $3.50 in his cart already. How much money does Eric have left to spend on his other groceries?Take your time figuring out the answer. When you’re ready, look below to check your solution with ours! Solution: The 4 boxes of cookies cost 4 ×$2.85 = $11.40. The cookies plus the milk cost$11.40 + $3.50 =$14.90. Subtracting $14.90 from$31.00, we get $16.10. • 11th-13th: Queen’s Birthday Weekend, Sat-Mon • 25th-27th: Christmas & Boxing Day Weekend, Sun-Tue • 28th-31st: Year End, Wed-Sat Recommended Reading: Michael Jackson Kids Biological Parents ## What Are Word Problems A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you’ve ever taken a math class, you’ve probably solved a word problem. For instance, does this sound familiar? Johnny has 12 apples. If he gives four to Susie, how many will he have left? You could solve this problem by looking at the numbers and figuring out what the problem is asking you to do. In this case, you’re supposed to find out how many apples Johnny has left at the end of the problem. By reading the problem, you know Johnny starts out with 12 apples. By the end, he has 4 less because he gave them away. You could write this as: 12 – 4 12 – 4 = 8, so you know Johnny has 8 apples left. ## Benefits Of Algebra Word Problems Worksheets We use algebra in our everyday life without even realising it. Solving algebraic word problems worksheets help kids relate and understand the relevance of algebra in the real world. Algebra finds its way while cooking, measuring ingredients, sports, finance, professional advancement etc. They help in logical thinking and help students to break down a problem and then find its solution. You May Like: How Did The Geography Affect The Development Of Greece ## Free Word Problems For Math Intervention Activities Is it a challenge for your students to break down word problems? Do they struggle with identifying the operation, solving the problem, justifying their answer, or all of the above? This can definitely be a challenge for your students and you when this happens . This post will share some strategies for teaching word problems and a set of free word problems that are perfect for math intervention activities and remediation. ## Strategies For Word Problem Math Intervention Here are some of the strategies and activities that I use to support my students with word problems: • Introduce new math problems with a context in the form of a relatable word problem • Expose my students to a variety of word problems regularly and consistently > The free set of word problems will help with this. • Model my thinking when reading and solving word problems • Provide my students with a step-by-step way to work through understanding and solving a word problem > The free set of word problems will help with this. • Get hands-onuse hands-on sorts and moveable digital activities to have my students interact with word problems > The free set of word problems will help with this. • Teach situations and contexts and not key words when it comes to determining the operation needed. • Allow for opportunities for students to share and discuss word problem solving strategies • Now, lets take a look at the free set of word problems that will give you some free math intervention activities to help your students master word problems. You May Like: Geometry Answers Mcdougal Littell ## Math Intervention Word Problems Sort Activity Word problems are a difficult math skill to make hands-on but anytime I can make something hands-on, the better my students do. The second set of word problems included in this free resource are for a sort activity where the students sort six word problems by operation . You can use this to focus just on understanding the problems and determining the operation or you can take it a step further and have the students solve the problems after sorting. ## Analysis Of The Solution The cost to produce 50,000 units is$77,500, and the revenue from the sales of 50,000 units is also $77,500. To make a profit, the business must produce and sell more than 50,000 units. Figure 11 We see from the graph in Figure 12 that the profit function has a negative value until x=50,000, when the graph crosses the x-axis. Then, the graph emerges into positive y-values and continues on this path as the profit function is a straight line. This illustrates that the break-even point for businesses occurs when the profit function is 0. The area to the left of the break-even point represents operating at a loss. Figure 12 Recommended Reading: Chapter 7 Quiz 1 Geometry ## Math Intervention Word Problems Graphic Organizer Activity The first set of word problems includes 10 multiplication and division word problems with a graphic organizer. The organizer helps students break down the steps of solving the word problem. The graphic organizer for each problem asks the students to: • Retell the problem • Select the operation and reason for selecting that operation • Solve the problem • Defend why the answer makes sense • Prove the answer I have also included the word problems in a copy friendly version with 8 word problems on a page and blank templates of the graphic organizer. You can use laminated copies of the blank template and have students write on them with dry erase markers. This makes it super easy to use during stations and guided math groups. Note: It can be time-consuming to complete all parts of the graphic organizer each time if used regularly. Feel free to have students only complete specific sections as needed. You could even start with just having them retell the problem, select the operation, and then solve the problem. Then you can move to the other sections later on. Alternatively, you can skip the retelling and focus on the defending and proving sections. ## Solution: Find The Break Systems of equations word problems example 1 | Algebra I | Khan Academy  Find the break-even quantity for a company that makes X number of computer monitors at a cost C given by C = 870 + 70x and receives revenue R given by R = 105xStep 1. Breakeven points, set the equations C=180+70x and R=105x to be equal.Step 2. Then, 870+70x=105x.Step 3. The following steps will solve the equation in Step 2.Subtract 70x from both sides of the equation to get x-terms only on the right side.Divide 35 to both sides of the equation or x is approximately 25 computers must be sold to break evenStep 4. ANSWER is 25 computers must be sold to break even with a positive profit.I hope the above steps and explanation were helpful.For free Step-By-Step Videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry, please visit http://www.FreedomUniversity.TV/courses/Trigonometry.Also, good luck in your future studies. Respectfully, Don’t Miss: Books Never Written Pre Algebra With Pizzazz ## Word Problems In Algebra If you were able to solve this problem, you should also be able to solve algebra word problems. Yes, they involve more complicated math, but they use the same basic problem-solving skills as simpler word problems. You can tackle any word problem by following these five steps: • Read through the problem carefully, and figure out what it’s about. • Represent unknown numbers with variables. • Translate the rest of the problem into a mathematical expression. • Solve the problem. • Check your work. • We’ll work through an algebra word problem using these steps. Here’s a typical problem: The rate to rent a small moving van is$30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took two days, and the van cost$360. How many miles did she drive?

It might seem complicated at first glance, but we already have all of the information we need to solve it. Let’s go through it step by step.

#### Step 1: Read through the problem carefully.

With any problem, start by reading through the problem. As you’re reading, consider:

• What question is the problem asking?
• What information do you already have?

Let’s take a look at our problem again. What question is the problem asking? In other words, what are you trying to find out?

The rate to rent a small moving van is $30 per day, plus$0.50 per mile. Jada rented a van to drive to her new home. It took 2 days, and the van cost \$360. How many miles did she drive?

#### Step 2: Represent unknown numbers with variables.

30 â2 + .5 âm = 360

 60

## Things To Do: Next Time When Your Children Are Solving Word Problems

• Read word problems several times slowly and carefully to ensure that all students understand.
• Break the problem down into smaller chunks if possible.
• Allow students to act out word problems to better understand what theyre being asked to do.
• To assist students in visualising the problem, provide manipulatives.
• Take field or walking trips to determine distances, speeds, and the area covered, among other things.
• To figure out percentages, differences, and higher-order math skills, have students complete surveys, interviews, and hands-on research in real-world situations.
• Allow students to create diagrams or drawings to aid in their understanding of problems.
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## How Do You Calculate The Break

The calculation is fairly simple. You need to use the following formula:

Often times, when it comes to the concept of the break even point in accounting, what is considered is the cash sales associated to the break-even point level of sales, instead of the break-even point instead.

Notice from the break even price formula that denominator has \. So what happens when \? In that case the break-even point is infinity, in which case, the conclusion is that when the price equals the variable cost per unit, then there is no break even point.