Question

the product of three times a number and 9

Answer 1

Answer:

Three times the sum equals nine times the difference.

3(x + y) = 9(x - y)

3x + 3y = 9x - 9y

3y = 6x - 9y

12y = 6x

2y = x

The product of two numbers is equal to three times their sum.

xy = 3x + 3y

Since x = 2y, substitute 2y for x in this equation.

2y^2 = 6y + 3y

2y^2 = 9y

2y^2 - 9y = 0

Factor it.

y(2y - 9) = 0

y = 0, 9/2 or 4.5

Since x = 2y

x = 0, 9

Check it.

xy = 9 x 4.5 = 40.5

3(9 + 4.5) = 40.5

9(9 - 4.5) = 40.5

It checks.