Question
(b) Given that \( \frac{5 a-3 b}{2 a}=\frac{4}{3} \), find the ratio of \( a: b \).
Ask by Chadwick Wells. in Singapore
Jan 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The ratio of \( a \) to \( b \) is \( 9:7 \).
Solution
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The Deep Dive
To solve the equation \( \frac{5 a-3 b}{2 a}=\frac{4}{3} \), we can cross-multiply: \[ 3(5a - 3b) = 4(2a) \] Expanding both sides yields: \[ 15a - 9b = 8a \] Now, let's rearrange the equation by moving \(8a\) to the left: \[ 15a - 8a - 9b = 0 \] \[ 7a - 9b = 0 \] Now, we can express this in terms of the ratio \( a:b \): \[ 7a = 9b \] Dividing both sides by \(b\) and \(7\): \[ \frac{a}{b} = \frac{9}{7} \] Thus, the ratio \( a : b \) is \( 9 : 7 \).
