Let's break down the problem step-by-step to find the store's cost for the shirt.
### Step 1: Determine the Sale Price
The regular price of the shirt is [tex]$11.70. The sale price is described as being 80% less than the regular price. To find the sale price:
1. Calculate 80% of the regular price:
\[
0.80 \times 11.70 = 9.36
\]
2. Subtract this amount from the regular price:
\[
11.70 - 9.36 = 2.34
\]
So, the sale price of the shirt is $[/tex]2.34.
### Step 2: Relate the Sale Price to the Store's Cost
The sale price is also described as being 30% greater than the store's cost. We can express this relationship with the following equation:
[tex]\[
\text{Sale Price} = \text{Store's Cost} + 0.30 \times \text{Store's Cost}
\][/tex]
[tex]\[
\text{Sale Price} = 1.30 \times \text{Store's Cost}
\][/tex]
We already know the sale price is [tex]$2.34. Let \( x \) be the store's cost. Using the sale price equation:
\[
2.34 = 1.30 \times x
\]
### Step 3: Solve for the Store's Cost
To isolate \( x \), divide both sides of the equation by 1.30:
\[
x = \frac{2.34}{1.30}
\]
\[
x \approx 1.80
\]
So, the store's cost for the shirt was approximately $[/tex]1.80.
### Summary
By following these steps, we found:
1. The sale price of the shirt is [tex]$2.34.
2. This sale price is 30% greater than the store's cost.
3. Therefore, the store's cost is approximately $[/tex]1.80.
So, the store's cost in dollars for the shirt is $1.80.
