Word Problem Involving Three Consecutive Even Integers

Find the product of three consecutive even integers whose sum is 42.

x = first integer
x + 2 = second consecutive even integer
x + 4 = third consecutive even integer   {consecutive even integers increase by 2} 

x + x + 2 + x + 4 = 42   {their sum is 42}
3x + 6 = 42   {combined like terms}
3x = 36   {subtracted 6 from each side}
x = 12   {divided each side by 3}
x + 2 = 14   {substituted 12, in for x, into x + 2}
x + 4 = 16   {substituted 12, in for x, into x + 4} 

the three integers are 12, 14, and 16 

Their product
= 12 x 14 x 16   {product means multiply}
= 2688   {multiplied}


- Algebra House