Question

one integer is 7 more than another. their product is 228. find the integers.

smaller integer =
larger integer =

Explanation:

Define variables for the integers

Using the Integer Word Problems knowledge point
Let \(x\) represent the smaller integer.
The larger integer is \(x + 7\).

Set up the quadratic equation

Using the Integer Word Problems knowledge point

$$ x(x + 7) = 228 $$

$$ x^2 + 7x - 228 = 0 $$

Solve the quadratic equation by factoring

Using the Factoring Quadratic Equations and Solving Quadratic Equations knowledge points

$$ (x - 12)(x + 19) = 0 $$

$$ x = 12 \quad \text{or} \quad x = -19 $$

Determine the pairs of integers

Using the Integer Word Problems knowledge point
If \(x = 12\):
Smaller integer is \(12\), larger integer is \(12 + 7 = 19\).

If \(x = -19\):
Smaller integer is \(-19\), larger integer is \(-19 + 7 = -12\).

Answer:

One integer is 7 more than another. Their product is 228. Find the integers.

smaller integer = <blank>\(12\)</blank> or <blank>\(-19\)</blank>
larger integer = <blank>\(19\)</blank> or <blank>\(-12\)</blank>