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