If 3x + 5y = 52 and 32x-2 + 5y+1 = 206 where x and y are integers, find x + y.
Explanation:
Let 3x = a and 5y = b
⇒ 3x + 5y = 52 ⇒ a + b = 52
Also, 32x-2 + 5y+1 = 206 ⇒ 32x/9 + 5 × 5y = 206 ⇒ 32x + 45 × 5y = 1854 ⇒ a2 + 45b = 1854 ...(2)
(2) - 45 × (1)
⇒ a2 - 45a = 1854 - 2340 ⇒ a2 - 45a + 486 = 0 ⇒ (a - 18)(a - 27) = 0 ⇒ a = 18 or 27
⇒ 3x = 18 or 27 Since x is an integer, 3x = 27 and x = 3.
Also, b = 5y = 52 - 27 = 25, hence, y = 2
∴ x + y = 3 + 2 = 5.
Hence, option (c).
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