Integer Word Problems


To master this topic, you will need to know how to:
Consecutive integers are integers that follow each other when counting by ones.
14,15,16 are consecutive integers     14,17,20 are not consecutive integers
Consecutive even integers are integers that follow each other when counting by evens and consecutive odd integers are when you count by odds.
-14,-12,-10 are consecutive even integers     7,9,11 are consecutive odd integers


Example 1: Consecutive odd integers

Solve. Separate your answers by commas. Example: 2,5
The sum of two odd consecutive integers is -16. Find the two integers.

1.  Assign variables and translate the sentence into an equation.
Let x = one integer
Let x + 2 = next odd integer
sum of two odd consecutive integers is -16
x + (x + 2) = -16
2.  Solve.
x + (x + 2) = -16
2x + 2 = -16
2x = -18
x = -9
x + 2 = -7
3.  Double check.
Does -9 + (-7) = -16?   Yes!

The answer is


Example 2: Products

Solve. Separate your answers by commas. Example: 2,5
Six more than an integer times five less than the integer is 42. Find all possible solutions.

1.  Assign variables and translate the sentence into an equation.
Let x = integer
six more than an integer times five less than the integer is 42
(x + 6) × (x - 5) = 42
2.  Solve.
(x + 6)(x - 5) = 42
x2 + x - 30 = 42
x2 + x - 72 = 0
(x + 9)(x - 8) = 0
x = -9, 8
3.  Double check.
Does (-9 + 6)(-9 - 5) = (-3)(-14) = 42?   Yes!
Does (8 + 6)(8 - 5) = (14)(3) = 42?   Yes!

The answer is

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