Question

Two consecutive even integers have the following property. When the smaller integer is added to three times the larger integer, the result is two less than five times the smaller integer.

Rafael tries to model this scenario with the equation shown below. Unfortunately, Rafael has made an error on the left side of the equation. Explain what error he made.
n + 3n + 2 = 5n - 2
Write the correct equation (if you haven't already) and solve it to find the two consecutive even integers.

Answer 1

See below.

Explanation:

Let the smaller integer be n.

Then the larger integer is n + 2.

"When the smaller integer is added to three times the larger integer, the result is two less than five times the smaller integer."

The correct equation is:

n + 3(n + 2) = 5n - 2

His mistake is not using parentheses on the left side. Since he left out the parentheses, the left side is not "the smaller integer added to three times the larger integer", but rather it is "the smaller integer added to 2 plus 3 times the smaller integer."

n + 3(n + 2) = 5n - 2

n + 3n + 6 = 5n - 2

4n + 6 = 5n - 2

8 = n

n = 8

n + 2 = 10

The integers are 8 and 10.