Question

The difference between seven times a number and three time a second number is 25. The sum of twice the first and five times the second is 95. What are the numbers?

Answer 1

The numbers are 10 and 15

Solution:

Let the first number be "x"

Let the second number be "y"

The difference between seven times a number and three time a second number is 25

seven times the first number - three time a second number = 25

7(x) - 3(y) = 25

7x - 3y = 25 ------ eqn 1

The sum of twice the first and five times the second is 95

twice the first number + five times the second number = 95

2(x) + 5(y) = 95

2x + 5y = 95 ------- eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 1 by 2

14x - 6y = 50 ----- eqn 3

Multiply eqn 2 by 7

14x + 35y = 665 ------- eqn 4

Subtract eqn 3 from eqn 4

14x + 35y = 665

14x - 6y = 50

( - ) --------------------

41y = 665 - 50

41y = 615

y = 15

Substitute y = 15 in eqn 2

2x + 5y = 95

2x + 5(15) = 95

2x + 75 = 95

2x = 95 - 75

2x = 20

x = 10

Thus the numbers are 10 and 15