Question

Two sets of three consecutive integers have a property that the product of the larger two is

one less than 7 times the smallest. Set up and solve an equation that can be sue to find both
sets of integers. What are those sets of integers?

Answer 1

{1, 2, 3}, {3, 4, 5}

Explanation:

Write expressions for three consecutive integers: n, n + 1, n + 2.

Set up an equation for the verbal description: the product (mulitplication) of the two larger integers (the last two) is one less than 7 times the smallest (the first one).

(n + 1)(n + 2) = 7n - 1

Multiply (FOIL) the left side.

n^2 + 3n + 2 = 7n - 1

Subtract 7n and subtract 1 to make the right side 0.

n^2 - 4n + 3 = 0

Factor.

(n - 1)(n - 3) = 0

Set the two factors equal to 0

n - 1 = 0, n - 3 = 0

Solve for n.

n = 1, n = 3

One set of integers begins with 1, so it's {1, 2, 3}.

The other set begins with 3, so it's {3, 4, 5}