1.2 Commutative and Associative Properties
1.3 Identity and Inverse Properties
2.3 Fractions Equal to Whole Numbers
2.4 Converting Mixed and Improper Fractions
2.5 Adding and Subtracting Fractions with Like Denominators
2.6 Adding and Subtracting Fractions with Unlike Denominators
2.9 Understanding Keep, Change, Flip
3.1 Converting Fractions to Decimals
3.2 Converting Decimals to Fractions
3.3 Converting Integers to Decimals and Fractions
3.7 Understanding Proportional Ratios
3.8 Identifying Proportional Ratios
3.9 Comparing Ratios with Rates and Prices
3.11 Converting Percent to Fraction and Decimal
4.1 Operations and Expressions
4.3 Expressions with Addition and Subtraction
4.4 Expressions with Multiplication and Division
4.5 Expressions with Exponents
4.6 Expressions with Decimals and Fractions
4.10 Understanding Distributive Property
4.11 Using the Distributive Property
4.12 Combining Like Terms with Distributive Property
5.2 The Goal of Solving Equations
5.3 Checking the Answer to an Equation
5.4 Solving Equations with Addition and Subtraction
5.5 Solving Equations with Multiplication
5.6 Solving Equations with Division
5.7 Starting a Two-Step Equation
5.8 Solving Two-Step Equations
5.9 Simplifying and Solving Two-Step Equations
5.11 Translating Math Expressions
5.12 Translating Math Equations
5.13 Strategies for Algebraic Word Problems
6.2 Comparing Integers and Decimals
6.4 Graphing Inequalities on Number Lines
6.5 Writing Inequalities from Number Lines
6.6 Translating Inequalities from Word Problems
6.7 Solving Inequalities with Addition and Subtraction
6.8 Solving Inequalities with Multiplication and Division
6.9 Inequalities with Negative Numbers
6.10 Solving Inequalities with Negative Numbers
6.11 One-Step Inequality Word Problems
6.12 Writing Inequalities Different Ways
6.13 Solving Two-Step Inequalities
Math Basics > Unit 5 Equations > Lesson 5.14 Word Problems with "Total"
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Now we're going to look at solving word problems that have the word total. We'll see how we can write and solve equations to represent these word problems. When we think of the word total, we're normally taking different amounts of things and adding them together to see what the total amount is. So keep that in mind. As we solve this next problem. Carl and Benson have a total of 19 video games. If Carl has eight games, how many does Benson have? Before we set up our equation to solve this problem, let's make sure that we understand what's going on in the problem. Let's see. We have two people, carl and Benson. They have a total of 19 video games. Carl has eight games, but we don't know how many Benson has. So it looks like that's what we're being asked to find. How many does Benson have? That's very important for us to know so that we can set up our equation. But let's see what all the information is that we need to look for. We need to look for information to set up our variable. And that's going to be based on the question which we just said is, how many video games does Benson have? So we just need to use a variable to represent that unknown number. Let's use B, since Benson starts with B, but you could use any variable that you want. Next, we want to look for numbers in the word problem and make sure that we know what those numbers represent. The first number we come across is 19 for the total of the video games. That's important. Let's write that down. 19 equals the total video games. The other number we have is eight. That represents how many video games Carl has. So let's jot that down. Eight equals the video games that Carl has. Now, we had mentioned that when we see the word total in a math problem, that means we're adding different values together, and that will equal the total. So what we're going to do is take the number of video games that Benson has, which is B, and we're going to add that with the number of video games that Carl has, which is eight, and then we're going to use an equal sign to show that that total represents 19 video games. So, putting it all together, we have B plus eight equals 19. Great. There's our equation. Now we just need to solve for our variable B. So we need to isolate B, which means that we need to undo the plus eight. So we'll subtract eight on both sides. Now we'll simplify both sides of that equation. On the left side, we have B plus eight, and then minus eight, the plus eight minus eight will cancel each other out to equal just zero. So that left side will become B plus zero. And on the right, we have 19 minus eight, which is eleven. So there we go. B plus zero equals eleven. But do we really have to put that zero in there? Not really. Whenever we add zero to something, it doesn't change its value. So we can simplify this even more. To B equals eleven, our equation is solved. We have our variable B by itself, it's isolated on one side We have equal sign in the middle and our number, which is our solution by itself on the other side of the equal sign. So our equation is solved. Now, how does this relate to our word problem? Well, since represents the number of video games that Benson has, we now know that Benson has eleven video games. So there you go. We just followed a step by step strategy that helped us set up an equation to solve this word problem.
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