The sum of two numbers is 63. Three times the smaller number is 14 more than twice the larger number. Find the numbers.

Question

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Answer 1

The answers are 28 smaller and 35 larger.

X = smaller number

63 - X = larger number

Three times the smaller number = 3X

14 more than twice the larger number = 2(63-X) + 14

3X = 2(63 - X) + 14

3X = 126 - 2X + 14

+2X +2X

5X = 140

/5 / 5

X = 28 smaller number

63 - 28 = 35 larger number

Answer 2

n = smaller, m = larger

n + m = 63

3n = 2m + 14

 

Solve for n and m.

 

n = 63 - m

3(63 - m) = 2m + 14

189 - 3m = 2m + 14

175 = 5m

m = 35

n = 63 - m = 63 - 35 = 28

 

Test the answers.