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 number
Their 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 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.
- 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
- 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 number
Their 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 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
- 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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