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The sum of two numbers is 20 and the sum of their reciprocals is 5/24. Find the larger number.

Competition practiceAlgebra

A12
B8
C16
D10

Step-by-Step Solution

(x + y) / x y = 5/24

gives

x y = 20 \times 24/5 = 96

. The numbers are the roots of

t^{2} - 20 t + 96 = 0

: 12 and 8.

Answer: A) 12

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