Difference between revisions of "1982 AHSME Problems/Problem 5"
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Since we know <math>a</math> is less than <math>b</math> and <math>\frac{x}{y}=\frac{bc}{a+b}</math>, the smaller of <math>x</math> and <math>y</math> must be <math>x</math>. Therefore the answer is <math>\boxed{\textbf{(C) }\frac{ac}{a+b}}</math>. | Since we know <math>a</math> is less than <math>b</math> and <math>\frac{x}{y}=\frac{bc}{a+b}</math>, the smaller of <math>x</math> and <math>y</math> must be <math>x</math>. Therefore the answer is <math>\boxed{\textbf{(C) }\frac{ac}{a+b}}</math>. | ||
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Latest revision as of 19:06, 25 March 2020
Problem
Two positive numbers and are in the ratio where . If , then the smaller of and is
Solution
We can write 2 equations.
and
Solving for and in terms of we get :
and
Since we know is less than and , the smaller of and must be . Therefore the answer is .
~superagh