Question
Two numbers are such that if 12 is subtracted from each,
the resulting numbers are in the ratio 7 : 9. If the sum of the original numbers is 216, find the numbers.Solution
Let the numbers be x and y. Given: (x − 12) : (y − 12) = 7 : 9 ⇒ (x − 12)/(y − 12) = 7/9 ⇒ 9(x − 12) = 7(y − 12) ⇒ 9x − 108 = 7y − 84 ⇒ 9x − 7y = 24 …(1) Also, x + y = 216 …(2) From (2): x = 216 − y Substitute into (1): 9(216 − y) − 7y = 24 1944 − 9y − 7y = 24 1944 − 16y = 24 16y = 1944 − 24 = 1920 y = 1920 / 16 = 120 Then x = 216 − 120 = 96 Answer: The numbers are 96 and 120
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