Question

Find two numbers such that 6 times the first and 7 times the second equals 277 and 9 times the first and 4 times the second equals 253

Answer 1

Let us assume, x and y are the two numbers.

Given:

6x + 7y = 277 --------------1

And

9x + 4y = 253 --------------2

Multiply the equation 1 by 3 and equation 2 by 2

18x + 21y = 831----------------3

And

18x + 8y = 506 ------------4

Subtract equation 4 from equation 3

13y = 325

y = 25

Substitute the value of y in equation 1

6x + 7 * 25 = 277

6x = 277 – 175

6x = 102

x = 17

The two numbers are 17 and 25.