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 8, 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)}\quad 16 \qquad \text{(B)}\quad 24 \qquad \text{(C)}\quad 32 \qquad \text{(D)}\quad 44 \qquad \text{(E)} \quad 52 </math> | <math>\text{(A)}\quad 16 \qquad \text{(B)}\quad 24 \qquad \text{(C)}\quad 32 \qquad \text{(D)}\quad 44 \qquad \text{(E)} \quad 52 </math> | ||
| Line 10: | Line 10: | ||
<cmath> 3y = 4x </cmath> | <cmath> 3y = 4x </cmath> | ||
| − | 2) The difference between the number is 8. | + | 2) The difference between the number is <math>8</math>. |
<cmath> y - x = 8 </cmath> | <cmath> y - x = 8 </cmath> | ||
| − | Solving this system of equation yields <math>x = 24</math> and <math>y = 32 | + | Solving this system of equation yields <math>x = 24</math> and <math>y = 32</math>. The answer is <math>\text{C}.</math> |
| + | |||
| + | ==See also== | ||
| + | |||
| + | {{AHSME box|year=1981|num-b=3|num-a=5}} | ||
| + | |||
| + | {{MAA Notice}} | ||
Latest revision as of 13:32, 28 June 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 the smaller number be 
and the larger number be 
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.
![\[3y = 4x\]](http://latex.artofproblemsolving.com/2/8/1/281479c145aed9c6e6c343c5bc90cb2b0e1d57d9.png)
2) The difference between the number is .
![\[y - x = 8\]](http://latex.artofproblemsolving.com/b/2/8/b284ce90dc2e412401ead7aa82d9e7c69c0ca18b.png)
Solving this system of equation yields 
and 
. The answer is 
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. 
