Question
Jose is saving money to buy a game. So far he has saved \( \$ 6 \), which is two-thirds of the total cost of the game. How much does the game cost?
Ask by Stephens Deleon. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The game costs \$9.
Solution
To determine the total cost of the game, let's break down the problem step by step.
**Given:**
- Jose has saved **\$6**.
- This amount represents **two-thirds (2/3)** of the total cost of the game.
**Let’s denote the total cost of the game as \( C \).**
According to the problem:
\[
\frac{2}{3} \times C = 6
\]
**To find \( C \), follow these steps:**
1. **Set Up the Equation:**
\[
\frac{2}{3}C = 6
\]
2. **Solve for \( C \):**
- Multiply both sides of the equation by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \), to isolate \( C \):
\[
C = 6 \times \frac{3}{2}
\]
3. **Calculate the Value:**
\[
C = 6 \times 1.5 = 9
\]
**Conclusion:**
The total cost of the game is **\$9**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find out the total cost of the game, we can set up an equation. Since Jose has saved \( \$ 6 \), and that amount represents two-thirds of the total cost, we can use the formula: \[ \text{Total Cost} = \frac{\text{Amount Saved}}{\text{Fraction Saved}} = \frac{6}{\frac{2}{3}}. \] Inverting the fraction gives us: \[ \text{Total Cost} = 6 \times \frac{3}{2} = 9. \] So, the game costs \( \$ 9 \). Keep saving, Jose! You'll have that game in no time!
