Difference between revisions of "1964 AHSME Problems/Problem 23"
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<math>\textbf{(A)}\ 6\qquad \textbf{(B)}\ 12\qquad \textbf{(C)}\ 24\qquad \textbf{(D)}\ 48\qquad \textbf{(E)}\ 96</math> | <math>\textbf{(A)}\ 6\qquad \textbf{(B)}\ 12\qquad \textbf{(C)}\ 24\qquad \textbf{(D)}\ 48\qquad \textbf{(E)}\ 96</math> | ||
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Set the two numbers as <math>x</math> and <math>y</math>. Therefore, | Set the two numbers as <math>x</math> and <math>y</math>. Therefore, |
Latest revision as of 03:00, 19 June 2019
Problem
Two numbers are such that their difference, their sum, and their product are to one another as . The product of the two numbers is:
Solution
Set the two numbers as and . Therefore, , and . Simplifying the first equation gives . Substituting for in the second equation gives Solving yields or . Substituting back into the first equation yields which is false, so is not valid and . Substituting into gives and .
See More
1964 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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All AHSME Problems and Solutions |
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