Question
If (9x + 4y) = 808 and 2x:5y = 18:25, then find the
value of (2x² + 3y²).Solution
Given, 2x:5y = 18:25 Or, 2x × 25 = 5y × 18 Or, 50x = 90y So, x:y = 9:5 So, let the values of 'x' and 'y' be '9k' and '5k', respectively. ATQ, (9x + 4y) = 808 Or, 9 × 9k + 4 × 5k = 808 Or, 81k + 20k = 808 Or, 101k = 808 So, 'k' = 8 Therefore, values of 'x' and 'y' are 72 and 40, respectively. So, (2x² + 3y²) = (2 × 72² + 3 × 40²) = (2 × 5184 + 3 × 1600) = (10368 + 4800) = 15,168 Hence, option d.
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