Certainly! Let's walk through the solution step by step:
1. Define the given information:
- Store A offers a 15% discount.
- Store B offers a 25% discount.
- Heather saves [tex]$15 more by buying the computer at Store B instead of Store A.
2. Let \( x \) be the sticker price of the computer.
3. Calculate the savings at each store:
- At Store A, the savings are \( 15\% \) of \( x \):
\[
\text{savings at Store A} = 0.15 \times x
\]
- At Store B, the savings are \( 25\% \) of \( x \):
\[
\text{savings at Store B} = 0.25 \times x
\]
4. Set up the equation based on the difference in savings:
- Heather saves $[/tex]15 more by buying the computer at Store B, so:
[tex]\[
\text{savings at Store B} - \text{savings at Store A} = 15
\][/tex]
- Substitute the savings into the equation:
[tex]\[
0.25x - 0.15x = 15
\][/tex]
5. Simplify the equation:
[tex]\[
(0.25 - 0.15)x = 15
\][/tex]
[tex]\[
0.10x = 15
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{15}{0.10}
\][/tex]
[tex]\[
x = 150
\][/tex]
7. Check if [tex]\( x = 150 \)[/tex] matches any of the given options:
[tex]\[
\text{Options given are: } 500, 650, 750, 850
\][/tex]
- Clearly, [tex]\( x = 150 \)[/tex] does not match any of the provided options.
After analyzing, we realize that the solution (None) does not provide any matching sticker price options as requested in the problem. This leads us to conclude that there might be an error in the listed options or a misunderstanding in the problem setup. Thus, based on the calculations and given options, there is no suitable sticker price that satisfies all the conditions.
