Question

Jackie is thinking of one number and Adrian is thinking of another. Camila thought if I take these two numbers, they have a product of 567 and a difference of six. Jackie’s number is higher than Adrian’s. What are Jackie’s and Adrian’s numbers?

Answer 1

• Jackie: 27
• Adrian: 21

Explanation:

Integers with a product of 567 are ...

567 = 1·567 = 3·189 = 7·81 = 9·63 = 21·27

The last of these pairs of factors have a difference of 6, so they are the answers.

Jackie's number is 27; Adrian's number is 21.

_____

You could let "a" represent Adrian's number and write the equation ...

a(a +6) = 567

a^2 +6a +9 = 576 . . . . . complete the square

(a +3)^2 = 24^2 . . . . . . . write as squares

a = -3 +24 = 21 . . . . . . . . take the positive square root; subtract 3

Adrian's number is 21; Jackie's number is 27.