Question
At Handy Hardware Shop's annual spring-cleaning sale, every ratchet set in the shop gets marked down. Austin purchased 2 ratchet sets during the sale: one for himself and one to give to his dad on Father's Day. Each ratchet set cost $8 less than its full price. He paid a total of $56. What is the cost of each ratchet set at full price?
Answers
GPT-4o mini
Let the full price of each ratchet set be denoted as \( p \). According to the problem, each ratchet set is marked down by $8, so the sale price of each ratchet set can be expressed as \( p - 8 \).
Austin purchased two ratchet sets. Therefore, the total amount he paid can be calculated as:
\[
2 \times (p - 8)
\]
We know from the problem statement that Austin paid a total of $56. Thus, we can set up the equation:
\[
2(p - 8) = 56
\]
Next, we can simplify this equation. First, distribute the 2:
\[
2p - 16 = 56
\]
Now, add 16 to both sides of the equation to isolate the term with \( p \):
\[
2p = 56 + 16
\]
\[
2p = 72
\]
Now, divide both sides by 2 to solve for \( p \):
\[
p = \frac{72}{2}
\]
\[
p = 36
\]
Thus, the full price of each ratchet set is \( \boxed{36} \).
Austin purchased two ratchet sets. Therefore, the total amount he paid can be calculated as:
\[
2 \times (p - 8)
\]
We know from the problem statement that Austin paid a total of $56. Thus, we can set up the equation:
\[
2(p - 8) = 56
\]
Next, we can simplify this equation. First, distribute the 2:
\[
2p - 16 = 56
\]
Now, add 16 to both sides of the equation to isolate the term with \( p \):
\[
2p = 56 + 16
\]
\[
2p = 72
\]
Now, divide both sides by 2 to solve for \( p \):
\[
p = \frac{72}{2}
\]
\[
p = 36
\]
Thus, the full price of each ratchet set is \( \boxed{36} \).