Difference between revisions of "1981 AHSME Problems/Problem 4"
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==Problem== | ==Problem== | ||
| − | If three times the larger of two numbers is four times the smaller and the difference between the numbers is <math>8</math>, the the larger of two numbers is | + | If three times the larger of two numbers is four times the smaller and the difference between the numbers is <math>8</math>, the the larger of two numbers is |
| − | <math>\text{(A)}\ | + | <math>\text{(A)}\ 16 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 44 \qquad \text{(E)} \ 52 </math> |
==Solution== | ==Solution== | ||
| − | Let the smaller number | + | Let <math>x</math> be the smaller number and <math>y</math> be the larger number. Then <math>3y = 4x</math>, so <math>x = \frac{3}{4}y</math>. Also, <math>y - x = 8</math>, so <math>y - \frac{3}{4}y = \frac{1}{4}y = 8</math>, and <math>y = \boxed{(\textbf{C})\ 32}</math>. |
| − | + | ==See also== | |
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| − | + | {{AHSME box|year=1981|num-b=3|num-a=5}} | |
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| − | {{AHSME box|year=1981| | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 15:57, 18 August 2025
Problem
If three times the larger of two numbers is four times the smaller and the difference between the numbers is 
, the the larger of two numbers is
Solution
Let 
be the smaller number and 
be the larger number. Then 
, so 
. Also, 
, so 
, and 
.
See also
| 1981 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
