**Mathematical Reasoning in Word Problems Practice Problems**

**Set 1: Consecutive Integers that Differ by One**

To review word problems that require mathematical reasoning, go to Mathematical Reasoning in Word Problems Help

**Practice**

- Find two consecutive numbers whose sum is 57.
- Find three consecutive numbers whose sum is 48.
- Find four consecutive numbers whose sum is 90.

**Solutions**

- Let
*x*= first number.*x*+ 1 = second numberTheir sum is 57, so

*x*+ (*x*+ 1) = 57.The first number is 28 and the second is

*x*+ 1 = 28 + 1 = 29. - Let
*x*= first number.*x*+ 1 = second number*x*+ 2 = third numberTheir sum is 48, so

*x*+ (*x*+ 1) + (*x*+ 2) = 48.The first number is 15; the second,

*x*+ 1 = 15 + 1 = 16; and the third,*x*+ 2 = 15 + 2 = 17. - Let
*x*= first number.*x*+ 1 = second number*x*+ 2 = third number*x*+ 3 = fourth numberTheir sum is 90, so

*x*+ (*x*+ 1) + (*x*+ 2) + (*x*+ 3) = 90.The first number is 21; the second,

*x*+ 1 = 21 + 1 = 22; the third,*x*+ 2 = 21 + 2 = 23; and the fourth,*x*+ 3 = 21 + 3 = 24.

**Set 2: Consecutive Integers that Differ by More than One**

To review word problems that require mathematical reasoning, go to Mathematical Reasoning in Word Problems Help

**Practice**

- The sum of two numbers is 85. One number is 15 more than the other. What are the two numbers?
- The sum of two numbers is 48. One number is three times the other. What are the numbers?

**Solutions**

- Let
*x*= first number.*x*+ 15 = second numberTheir sum is 85, so

*x*+ (*x*+ 15) = 85.The numbers are 35 and

*x*+ 15 = 35 + 15 = 50. - Let
*x*= first number.3

*x*= second numberTheir sum is 48, so

*x*+ 3*x*= 48.The numbers are 12 and 3

*x*= 3(12) = 36.

**Set 3: Consecutive Inegers and Multiplying by Quantities**

To review word problems that require mathematical reasoning, go to Mathematical Reasoning in Word Problems Help

**Practice**

- The sum of two numbers is 10. Three times the smaller plus 5 times the larger number is 42. What are the numbers?
- The difference between two numbers is 12. Twice the smaller plus four times the larger is 108. What are the two numbers?
- The difference between two numbers is 8. The sum of one and a half times the smaller and four times the larger is 54. What are the numbers?
- The sum of two numbers is 11. When twice the larger is subtracted from 5 times the smaller, the difference is 6. What are the numbers?

**Solutions**

- Let
*x*represent the smaller number. The larger number is then 10 –*x*.The numbers are 4 and 10 –

*x*= 10 – 4 = 6. -
The difference between the numbers is 12, so one number is 12 more than the other. Let

*x*represent the smaller number. Then*x*+ 12 is the larger. Twice the smaller is 2*x*, and four times the larger is 4(*x*+ 12).2

*x*+ 4(*x*+ 12)= 108

2

*x*+ 4*x*+ 48= 108

6

*x*+ 48= 108

– 48

– 48

The smaller number is 10 and the larger is

*x*+ 12 = 10 + 12 = 22. - The difference between the numbers is 8, so one of the numbers is 8 more than the other. Let
*x*represent smaller number. The larger number is*x*+ 8. One and a half of the smaller number is ; four times the larger is 4(*x*+ 8).The smaller number is 4 and the larger,

*x*+ 8 = 4 + 8 = 12. - Let
*x*= smaller number. Then 11 –*x*is the larger. Five times the smaller is 5*x*, and twice the larger is 2(11 –*x*). “Twice the larger subtracted from 5 times the smaller” becomes “5*x*– 2(11 –*x*).”The smaller number is 4 and the larger is 11 –

*x*= 11 – 4 = 7.

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