Integer Word Problems Sample Problems

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Here are some tips for Integer Word Problems, which aligns with New York state standards:

Integer Word Problems

To master this topic, you will need to know how to:

translate sentences into equations (see here)
solve polynomials (see here)

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

six more than an integer	times	five less than the integer	is	42
(x + 6)	×	(x - 5)	=	42

(x + 6)(x - 5)	=	42
x² + x - 30	=	42
x² + x - 72	=	0
(x + 9)(x - 8)	=	0
x	=	-9, 8