Question

Two numbers are in the ratio 4 : 7. If thrice the larger be added to twice the smaller, the sum is 59. Find the numbers.

Answer 1

Let the smaller number be x and the larger number be y.
According to the question,
`x/y = 4/7`
7x = 4y
7x - 4y = 0                 ......(1)
and, 3y + 2x = 59      ......(2)

Multiplying equation no. (1) by 3 and (2) by 4.
21x - 12y = 0             ......(3)
8x + 12y = 236          .......(4)
Adding equation (3) and (4),
        21x - 12y = 0
+      8x + 12y = 236  
        29x = 236
           x = `236/29`
From (1)
`7(236/29) = 4y`

`y = 7(59/29)`   

`y = (413/29)`
Hence, the numbers are `236/29 and 413/29`.