What are the two numbers?

Question

The product of the two numbers is 30. The difference between the two numbers is 13. What are the two numbers?

Answer 1

Hi Charlotte, let x represent one of the numbers and y the other one. Set up a system of equations to represent the information given.

Product of two numbers:

x * y = 30

Difference of two numbers:

x - y = 13

Solve the second equation for x:

x = 13 + y

Substitute into product equation for x:

(13 + y) * y = 30

Solve for y:

y² + 13y = 30

Rewrite:

y² + 13y - 30 = 0

Factor:

(y + 15) * (y - 2) = 0

Use the zero product rule:

y + 15 = 0

y = -15

And

y - 2 = 0

y = 2

Solve using y = -15:

x * -15 = 30

x = -2

Answer:

The two numbers are -2 and -15.

Solve using y = 2:

x * 2 = 30

x = 15

Answer:

The two numbers are 2 and 15.

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