To find the original price of the gift, let's break down the problem step by step using the provided hint.
1. Understand the given information:
- Four sisters bought a gift for their mother.
- They received a 10% discount on the original price of the gift.
- After the discount, the total price was divided equally among the four sisters, with each sister paying [tex]$9.00.
2. Define the variable:
- Let \( P \) be the original price of the gift.
3. Express the discounted price:
- The discount amount is 10% of the original price, which is \( 0.1P \).
- Therefore, the discounted price is \( P - 0.1P = 0.9P \).
4. Set up the equation using the information about the equal payments:
- After the discount, the total amount paid was divided equally among the four sisters.
- Thus, each sister's share is \( \frac{0.9P}{4} \).
- According to the problem, each sister paid $[/tex]9.00.
5. Form the equation:
- Based on the above information, we have:
[tex]\[
\frac{0.9P}{4} = 9.00
\][/tex]
6. Solve the equation:
- To isolate [tex]\( P \)[/tex], first multiply both sides of the equation by 4:
[tex]\[
0.9P = 9.00 \times 4
\][/tex]
- Simplify the right side:
[tex]\[
0.9P = 36.00
\][/tex]
- Now, divide both sides by 0.9 to find [tex]\( P \)[/tex]:
[tex]\[
P = \frac{36.00}{0.9}
\][/tex]
- Simplify the division:
[tex]\[
P = 40.00
\][/tex]
7. Conclusion:
- The original price of the gift was $40.00.
