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Difference between revisions of "1981 AHSME Problems/Problem 4"

(Created page with "==Problem== If three times the larger of two numbers is four times the smaller and the difference between the numbers is 8, the the larger of two numbers is: <math>\text{(A)...")
 
(No difference)

Latest revision as of 15:48, 28 January 2021

Problem

If three times the larger of two numbers is four times the smaller and the difference between the numbers is 8, the the larger of two numbers is:

$\text{(A)}\quad 16 \qquad \text{(B)}\quad 24 \qquad \text{(C)}\quad 32 \qquad \text{(D)}\quad 44 \qquad \text{(E)} \quad 52$

Solution

Let the smaller number be $x$ and the larger number be $y.$ We can use the information given in the problem to write two equations:

1) Three times the larger of two numbers is four times the smaller. \[3y = 4x\]

2) The difference between the number is 8.

\[y - x = 8\]

Solving this system of equation yields $x = 24$ and $y = 32.$ The answer is $\text{C}.$

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