Question
Super Sprouts children's store is having its annual spring sale, when every item in the store gets marked down. During the sale, pajama sets sell for \( \$ 6 \) less than full price. Mrs. Rodriguez purchases 4 matching pajama sets: one for each of her children. She pays a total of \( \$ 68 \). How much does each pajama set cost at full price?
Ask by Sandoval Norton. in the United States
Dec 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The full price of each pajama set is $23.
Solution
Let the full price of each pajama set be denoted as \( p \). During the sale, the price of each pajama set is reduced by \( \$ 6 \), so the sale price is:
\[
p - 6
\]
Mrs. Rodriguez buys 4 pajama sets at the sale price, and she pays a total of \( \$ 68 \). Therefore, we can set up the following equation:
\[
4(p - 6) = 68
\]
Now, we will solve for \( p \). First, distribute the 4 on the left side:
\[
4p - 24 = 68
\]
Next, add 24 to both sides to isolate the term with \( p \):
\[
4p = 68 + 24
\]
\[
4p = 92
\]
Now, divide both sides by 4 to solve for \( p \):
\[
p = \frac{92}{4}
\]
\[
p = 23
\]
Thus, the full price of each pajama set is
\[
\boxed{23} \text{ dollars.}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
Let the full price of each pajama set be \( x \). During the sale, the pajama sets are sold for \( x - 6 \). Mrs. Rodriguez buys 4 pajama sets, so the total amount she pays is: \[ 4(x - 6) = 68 \] Now, let's distribute the 4: \[ 4x - 24 = 68 \] Next, add 24 to both sides to isolate the term with \( x \): \[ 4x = 68 + 24 \] \[ 4x = 92 \] Now, divide both sides by 4 to solve for \( x \): \[ x = \frac{92}{4} = 23 \] So, the full price of each pajama set is \( \$ 23 \).