Question

3) Find two numbers such that 5 times the larger plus 3 times the smaller is 47 and 4 times the larger minus twice the smaller is 20. T

Answer 1

Let the numbers are x and y

and x is larger than y

so, 5 times the larger + 3 times the smaller = 47

So, 5x + 3y = 47

And 4 times the larger - 2 the smaller = 20

so, 4x - 2y = 20

so, we have :

5x + 3y = 47 (1)

4x - 2y = 20 (2)

solve for x and y

Multiply eq.(1) by 2 and eq.(2) by 3

10x + 6y = 94

12x - 6y = 60

Add the last 2 equations:

22x = 154

x = 154/22 = 7

so,

5 * 7 + 3y = 47

3y = 47 - 5*7 = 12

y = 12/3 = 4

So, the numbers are 7 and 4