Question

Find 4 consecutive even integers where the product of the two smaller numbers is 72 less than the product of the two larger numbers.

Answer 1

Answer: 6, 8, 10, 12

Step-by-step explanation:

Given that x is the number, the 4 numbers would be

x, x + 2, x + 4, x + 6

so the two smallest numbers would be x and x + 2

and the two largest numbers would be x+4 and x+6

now set up an equation

x(x+2) = (x+4)(x+6) - 72

now FOIL

x^2 + 2x = x^2 + 6x + 4x + 24 - 72

combine like terms

x^2 + 2x = x^2 + 10x -48

subtract x^2 from both sides

2x = 10x - 48

subtract 2x from both sides

0 = 8x - 48

add 48 to both sides

48 = 8x

divide both sides by 8

6 = x

so the four numbers, x, x+2, x+4, and x+6 when you plug in x are equal to

6, 8, 10, 12