Question
The combined savings of Abel and Bahira are 15435 dinars. The savings of Bahira are \( 45 \% \) more than the savings of Abel. The savings of Bahira are \( \frac{3}{2} \) times the savings of Chanda. Work out the savings of Chanda.
Ask by Lowe Valdez. in Qatar
Jan 18,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Chanda has 6090 dinars in savings.
Solution
Let's denote the savings of Abel as \( A \), the savings of Bahira as \( B \), and the savings of Chanda as \( C \).
Given:
1. The combined savings of Abel and Bahira are 15435 dinars: \( A + B = 15435 \)
2. The savings of Bahira are \( 45\% \) more than the savings of Abel: \( B = 1.45A \)
3. The savings of Bahira are \( \frac{3}{2} \) times the savings of Chanda: \( B = \frac{3}{2}C \)
We can solve these equations to find the savings of Chanda.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}A+B=15435\\B=1.45A\\B=1.5C\end{array}\right.\)
- step1: Substitute the value of \(B:\)
\(\left\{ \begin{array}{l}A+1.45A=15435\\1.45A=1.5C\end{array}\right.\)
- step2: Simplify:
\(\left\{ \begin{array}{l}2.45A=15435\\1.45A=1.5C\end{array}\right.\)
- step3: Solve the equation:
\(\left\{ \begin{array}{l}A=6300\\1.45A=1.5C\end{array}\right.\)
- step4: Substitute the value of \(A:\)
\(1.45\times 6300=1.5C\)
- step5: Simplify:
\(9135=1.5C\)
- step6: Swap the sides:
\(1.5C=9135\)
- step7: Divide both sides:
\(\frac{1.5C}{1.5}=\frac{9135}{1.5}\)
- step8: Divide the numbers:
\(C=6090\)
- step9: Substitute the value of \(A:\)
\(B=1.45\times 6300\)
- step10: Simplify:
\(B=9135\)
- step11: Calculate:
\(\left\{ \begin{array}{l}A=6300\\B=9135\\C=6090\end{array}\right.\)
- step12: Check the solution:
\(\left\{ \begin{array}{l}A=6300\\B=9135\\C=6090\end{array}\right.\)
- step13: Rewrite:
\(\left(A,B,C\right) = \left(6300,9135,6090\right)\)
The savings of Chanda is 6090 dinars.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
Let's denote Abel's savings as \( A \) and Bahira's savings as \( B \). According to the problem: 1. \( A + B = 15435 \) 2. \( B = A + 0.45A = 1.45A \) Now, substituting \( B \) in the first equation: \[ A + 1.45A = 15435 \] \[ 2.45A = 15435 \] \[ A = \frac{15435}{2.45} \approx 6300 \] Now to find Bahira's savings: \[ B = 1.45A = 1.45 \times 6300 \approx 9135 \] Next, we can find Chanda's savings \( C \). Given that Bahira's savings are \( \frac{3}{2} \) times Chanda's savings: \[ B = \frac{3}{2}C \implies C = \frac{2}{3}B \] \[ C = \frac{2}{3} \times 9135 = 6090 \] Thus, Chanda's savings are **6090 dinars**.
