Question

one number is 6 more than another. the difference between their squares is 180. what are the numbers?

smaller number =

larger number =

Explanation:

Define the variables

Using the Integer Word Problems knowledge point
Let \(x\) represent the smaller number.
The larger number is \(x + 6\).

Set up the equation

Using the Square of a Binomial Sum knowledge point
The difference between their squares is 180:

$$ (x + 6)^2 - x^2 = 180 $$

Expand and simplify the equation

Using the Square of a Binomial Sum knowledge point

$$
LATEXBLOCK0
$$

Solve for the smaller number

Using the Integer Word Problems knowledge point

$$
LATEXBLOCK1
$$

Find the larger number

Using the Integer Word Problems knowledge point

$$
LATEXBLOCK2
$$

Answer:

One number is 6 more than another. The difference between their squares is 180. What are the numbers?

smaller number = <blank>12</blank>

larger number = <blank>18</blank>