Question

iscussion > cheating) 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.

Answer 1

Let the numbers are x and y

Given :

1) 5 times the larger + 3 times the smaller = 47

2) 4 times the larger - 2 times the smaller = 20

if the larger is x and the smaller is y

so, we have the following equations:

5x + 3y = 47 eq.(1)

4x - 2y = 20 eq.(2)

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

So,

10x + 6y = 94

12x - 6y = 60

Add the last two equations:

10x + 12x = 94 + 60

22x = 154

divide both sides by 22

x= 154/22 = 7

Substitute at eq.(1) with x to find y

5 * 7 + 3y = 47

35 + 3y = 47

3y = 47 - 35

3y = 12

divide both sides by 3

y = 12/3 = 4

So, the numbers are 7 and 4