Two numbers differ by 5. Seven times the smaller plus four times the larger is 108. Find the number

Step-by-step explanation:

Let the two numbers be x and y

If the two numbers differs by 5, then;

y-x = 5 ...1

x is the smaller

y is the larger

If seven times the smaller plus four times the larger is 108, this is expressed as;

7x + 4y = 108 ... 2

From 1;

y = 5 + x 3

Substitute 3 into 2;

From 2;

7x + 4y = 108

7x + 4(5+x) = 108

7x + 20 + 4x = 108

11x + 20 = 108

11x = 108-20

11x = 88

x = 88/11

x = 8

Since y = 5+x

y = 5 + 8

y = 13

hence the numbers are 8 and 13

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