Answer the word problem with a equation

Question

Three consecutive integers are n, n + 1 and n + 2. Four times the sum of the least and

greatest integers is 12 less than three times the less integer. What is the least integer?

Answer 1

Between n, n+1, and n+2, the least integer is n and the greatest integer is n+2. So, the sum of the least integer and the greatest integer is:

n + (n+2)

= n + n + 2

= 2n + 2

Four times this sum, by the distributive property, will be:

4(2n + 2)

= 8n + 8

Three times the less integer can be represented as 3n.

Since 8n + 8 is 12 less than 3n, we can represent this relationship through the equation:

(8n + 8) + 12 = 3n

Now we can solve for n using algebra.

8n + 8 + 12 = 3n

=> 8n +20 = 3n

-3n -3n

=> 5n + 20 = 0

-20 -20

=> 5n = -20

÷5 ÷5

=> n = -4

Since the least integer is n, the least integer must be -4.

Answer 2

This problem would be set up as 4[n + (n+2)] = 3n - 12 . This assumes that the final question is referring to the smallest integer.