Question
Exercise 1 1. Phiwe had R180. She spent \( \frac{2}{5} \) of her money on clothes and \( \frac{1}{3} \) on airtime. Calculate: 1.1 the fraction of the money she spent 1.2 the amount of money she has left.
Ask by Potter Daniels. in South Africa
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Phiwe spent \( \frac{11}{15} \) of her money and has R48 left.
Solution
**Step 1: Calculate the fraction of money spent**
Phiwe spent on clothes and airtime:
- Clothes: \( \frac{2}{5} \) of her money
- Airtime: \( \frac{1}{3} \) of her money
To find the total fraction spent, add the fractions:
\[
\frac{2}{5} + \frac{1}{3} = \frac{(2 \times 3) + (1 \times 5)}{15} = \frac{6 + 5}{15} = \frac{11}{15}
\]
**Step 2: Calculate the amount of money left**
The fraction of money left is:
\[
1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15}
\]
Since Phiwe started with R180, the amount left is:
\[
180 \times \frac{4}{15} = \frac{720}{15} = 48
\]
**Final Answers:**
1.1 The fraction of the money she spent is \( \frac{11}{15} \).
1.2 The amount of money she has left is R48.
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Simplify this solution Mind Expander
Phiwe first spends \( \frac{2}{5} \) of R180 on clothes, which amounts to \( R180 \times \frac{2}{5} = R72 \). Then, she spends \( \frac{1}{3} \) of her money on airtime, which is \( R180 \times \frac{1}{3} = R60 \). To find the total amount spent, simply add: \( R72 + R60 = R132 \). Hence, the fraction of money she spent is \( \frac{132}{180} = \frac{73}{90} \) after simplifying. To calculate how much money she has left, subtract the total amount spent from her initial amount: \( R180 - R132 = R48 \). Therefore, she has R48 remaining after her shopping spree!
