System of Linear Equations: Currency exchange: 3-variable system — NJC 2025 H2 Math Prelim Paper 1
What this question tests
Question
Paul is helping his friends to convert their foreign currencies back to Singapore Dollars. The amounts of foreign currencies converted, and the total amount received in Singapore Dollars are shown in the following table.
| Alex | Nicholas | Palmer | Maybelline | |
|---|---|---|---|---|
| US Dollar (USD) | 150 | 250 | 425 | \(a\) |
| Japanese Yen (JPY) | 5500 | 9500 | 1000 | 0 |
| Chinese Yuan (CNY) | 1000 | 2200 | 2000 | 1200 |
| Total amount: SGD | 419.30 | 797.20 | 913.10 | 568.40 |
However, he has forgotten the amount of US Dollar that Maybelline has passed to him. Assuming that, for each foreign currency, the exchange rate quoted for each of the friends is the same, calculate the value of \(a\).
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Let the exchange rates for US Dollar, Japanese Yen, and Chinese Yuan be \(U\), \(J\), and \(C\) Singapore Dollars respectively. \[\begin{aligned} 150U + 5500J + 1000C &= 419.30 \\ 250U + 9500J + 2200C &= 797.20 \\ 425U + 1000J + 2000C &= 913.10 \end{aligned}\]
Solving simultaneously by GC: \[ U = 1.2856, \quad J = 0.00862, \quad C = 0.17905. \]
For Maybelline: \[\begin{aligned} 1.2856a + 1200(0.17905) &= 568.40 \\ 1.2856a &= 568.40 - 214.86 = 353.54 \end{aligned}\]