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10 ## WORD PROBLEMSWORD PROBLEMS require practice in translating verbal language into algebraic language. See Lesson 1, Problem 8. Yet, word problems fall into distinct types. Below are some examples.
Example 1. Jane spent $42 for shoes. This was $14 less than twice what she spent for a blouse. How much was the blouse?
Let Here is the equation:
The blouse cost $28.
Example 2. There are (Although The problem states that "This" --
The solution here is not a number, because it will depend on the value of Example 3. The whole is equal to the sum of the parts. The sum of two numbers is 84, and one of them is 12 more than the other. What are the two numbers? We are told that the other number is 12 more, The problem states that their sum is 84: = 84 The line over We have:
This is the first number. Therefore the other number is
The sum of 36 + 48 is 84. Example 4. The sum of two consecutive numbers is 37. What are they?
Let The problem states that their sum is 37: = 37
The two numbers are 18 and 19. Example 5. One number is 10 more than another. The sum of twice the smaller plus three times the larger, is 55. What are the two numbers? Then the larger number is 10 more: The problem states:
That's the smaller number. The larger number is 10 more: 15. Example 6. Divide $80 among three people so that the second will have twice as much as the first, and the third will have $5 less than the second.
Then the second gets twice as much, 2 And the third gets $5 less than that, 2 Their sum is $80:
This is how much the first person gets. Therefore the second gets
The sum of 17, 34, and 29 is in fact 80. Example 7. Odd numbers. The sum of two consecutive odd numbers is 52. What are the two odd numbers?
An odd number is 1 more (or 1 less) than an even number. And so we represent an odd number as 2 Let 2
We will now solve that equation for
Therefore the first odd number is 2 Problems Problem 1. Julie has $50, which is eight dollars more than twice what John has. How much has John? (Compare Example 1.) First, what will you let To see the answer, pass your mouse over the colored area. The unknown number -- which is how much that John has. What is the equation?
2 Here is the solution:
Problem 2. Carlotta spent $35 at the market. This was seven dollars less than three times what she spent at the bookstore; how much did she spend there? Here is the equation.
3 Here is the solution:
Problem 3. There are Here is the equation.
2 Here is the solution:
Problem 4. Janet spent $100 on books. This was Here is the equation.
5 Here is the solution:
Problem 5. The whole is equal to the sum of the parts. The sum of two numbers is 99, and one of them is 17 more than the other. What are the two numbers? (Compare Example 3.) Here is the equation.
Here is the solution:
Problem 6. A class of 50 students is divided into two groups; one group has eight less than the other; how many are in each group? Here is the equation.
Here is the solution:
Problem 7. The sum of two numbers is 72, and one of them is five times the other; what are the two numbers? Here is the equation.
Here is the solution:
Problem 8. The sum of three consecutive numbers is 87; what are they? (Compare Example 4.) Here is the equation.
Here is the solution: 28, 29, 30. Problem 9. A group of 266 persons consists of men, women, and children. There are four times as many men as children, and twice as many women as children. How many of each are there? (What will you let
Here is the solution:
Problem 10. Divide $79 among three people so that the second will have three times more than the first, and the third will have two dollars more than the second. (Compare Example 6.) Here is the equation.
Here is the solution: $11, $33, $35. Problem 11. Divide $15.20 among three people so that the second will have one dollar more than the first, and the third will have $2.70 more than the second. Here is the equation.
Here is the solution: $3.50, $4.50, $7.20. Problem 12. Two consecutive odd numbers are such that three times the first is 5 more than twice the second. What are those two odd numbers? (See Example 7, where we represent an odd number as 2
Then the next one is 2 The problem states—that is, the equation is:
Therefore the first odd number is 2 And that is the true solution, because according to the problem:
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