If 9x − 3y = 96 and 4x : 3y = 20 : 21 , then find the value of 2x² + 3y².
Show answer & explanation
Correct answer: C
Explanation
Given:
9x − 3y = 96, 4x : 3y = 20 : 21
According to the formula:
Deriving a value from the ratio and substituting it into the other equation:
4x / 3y = 20 / 21
⇒ 4x × 21 = 3y × 20
⇒ 84x = 60y
⇒ 7x = 5y
⇒ y = (7/5)x
9x − 3y = 96
⇒ 9x − 3(7/5)x = 96
⇒ 9x − 21/5 x = 96
⇒ (45/5 − 21/5)x = 96
⇒ 24/5 x = 96
⇒ x = 96 × 5 / 24 = 20
⇒ y = (7/5) × 20 = 28
2x² + 3y² = 2×20² + 3×28²
= 2×400 + 3×784
= 800 + 2352
= 3152