Question
(11) Anna and Xinyi had an equal amount of money ot first. After Anna spent \( \$ 245 \) and Xinyl spent \( \$ 74 \), Xinyi had 4 times as muc money as Anna. How much money did each girl have at first?
Ask by Tucker Gough. in Singapore
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Each girl initially had $302.
Solution
Let's solve the problem step by step.
1. **Let’s define the initial amount each girl had:**
- Let \( x \) be the amount of money each Anna and Xinyi had initially.
2. **After their expenditures:**
- **Anna's remaining money:** \( x - 245 \) dollars
- **Xinyi's remaining money:** \( x - 74 \) dollars
3. **According to the problem, after spending, Xinyi had 4 times as much money as Anna:**
\[
x - 74 = 4(x - 245)
\]
4. **Solve for \( x \):**
\[
x - 74 = 4x - 980
\]
\[
-74 + 980 = 4x - x
\]
\[
906 = 3x
\]
\[
x = \frac{906}{3} = 302
\]
5. **Conclusion:**
- **Each girl initially had** \( \$302 \).
**Answer:** Each girl had $302 initially.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
Let the amount of money Anna and Xinyi had initially be \( x \). After spending, Anna has: \( x - 245 \) Xinyi has: \( x - 74 \) According to the problem, after spending, Xinyi has 4 times the amount of Anna: \[ x - 74 = 4(x - 245) \] Now, let's solve for \( x \): \[ x - 74 = 4x - 980 \] \[ -74 + 980 = 4x - x \] \[ 906 = 3x \] \[ x = 302 \] So, both Anna and Xinyi had \( \$ 302 \) at first. Just to double-check: After Anna spent \( \$ 245 \), she had \( 302 - 245 = 57 \). After Xinyi spent \( \$ 74 \), she had \( 302 - 74 = 228 \). Indeed, \( 228 \) is \( 4 \times 57 \), so both figures check out!
