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# Mathematical Reasoning in Word Problems Practice Problems

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## 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

1. Find two consecutive numbers whose sum is 57.
2. Find three consecutive numbers whose sum is 48.
3. Find four consecutive numbers whose sum is 90.

#### Solutions

1. Let x = first number.

x + 1 = second number

Their sum is 57, so x + ( x + 1) = 57.

The first number is 28 and the second is x + 1 = 28 + 1 = 29.

2. Let x = first number.

x + 1 = second number

x + 2 = third number

Their 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.

3. Let x = first number.

x + 1 = second number

x + 2 = third number

x + 3 = fourth number

Their 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

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

#### Solutions

1. Let x = first number.

x + 15 = second number

Their sum is 85, so x + ( x + 15) = 85.

The numbers are 35 and x + 15 = 35 + 15 = 50.

2. Let x = first number.

3 x = second number

Their 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

1. The sum of two numbers is 10. Three times the smaller plus 5 times the larger number is 42. What are the numbers?
2. The difference between two numbers is 12. Twice the smaller plus four times the larger is 108. What are the two numbers?
3. 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?
4. 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

1. Let x represent the smaller number. The larger number is then 10 – x .

The numbers are 4 and 10 – x = 10 – 4 = 6.

2. 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.

3. 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.

4. 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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