Question
1. Dorcas is 12 years old and her brother is 3 years older. Their father gives them pocket money in the ratio of their ages. If he has R 450 to give to them, what will each one get?
Ask by Pope Peters. in South Africa
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Dorcas gets R200 and her brother gets R250.
Solution
1. Let Dorcas's age be \(12\) and her brother's age be \(12 + 3 = 15\).
2. The ratio of their ages is therefore \(12:15\), which simplifies to:
\[
\frac{12}{15} = \frac{4}{5}
\]
So, the simplified ratio is \(4:5\).
3. Let each unit in the ratio be worth \(x\). Then:
\[
4x + 5x = 9x
\]
Since the total pocket money is \(450\), we have:
\[
9x = 450
\]
4. Solve for \(x\):
\[
x = \frac{450}{9} = 50
\]
5. Now, calculate the amount each receives:
- Dorcas gets:
\[
4x = 4 \times 50 = 200
\]
- Her brother gets:
\[
5x = 5 \times 50 = 250
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To find out how much pocket money each sibling receives, we first need to establish their ages and the ratio between them. Dorcas is 12 years old and her brother is 15 years old (12 + 3). The total age sum is 12 + 15 = 27. The ratio of their ages is therefore 12:15. Now, we can express their portions of the R 450 total according to this ratio. First, we add the parts of the ratio: 12 + 15 = 27 parts. For Dorcas: (12/27) * 450 = R 200. For her brother: (15/27) * 450 = R 250. So, Dorcas will receive R 200, and her brother will receive R 250.
