Question

The sum of a number and two times a smaller number is 62. Three times the bigger number exceeds the smaller number by 116.

The bigger number is
. The smaller number is
.

Answer 1

let x be the bigger and y the smaller of two numbers

⇒ x + 2y = 62 ... (eq 1)
3x - y = 116 ... (eq 2)

by multiplying through (eq 1) by 3 and (eq 2) by 1

[3 × (eq 1)] 3x + 6y = 186 ... (eq 1°)
[1 × (eq 2)] 3x - y = 116 ... (eq 2°)

by subtracting eq 2° from eq 1°

[eq 1° - eq 2°] 3x - 3x + 6y - (-y) = 186 - 116
⇒ 6y + y = 70
⇒ y = 10

By substituting y into eq 2

⇒ 3x - 10 = 116
⇒ 3x = 126
⇒ x = 42

∴ The bigger number is 42
AND The smaller number is 10