Difference between revisions of "1950 AHSME Problems/Problem 36"
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==Problem== | ==Problem== | ||
| − | A merchant buys goods at <math> 25\%</math> | + | A merchant buys goods at <math> 25\%</math> off the list price. He desires to mark the goods so that he can give a discount of <math> 20\%</math> on the marked price and still clear a profit of <math> 25\%</math> on the selling price. What percent of the list price must he mark the goods? |
<math>\textbf{(A)}\ 125\% \qquad | <math>\textbf{(A)}\ 125\% \qquad | ||
| Line 8: | Line 8: | ||
\textbf{(D)}\ 80\% \qquad | \textbf{(D)}\ 80\% \qquad | ||
\textbf{(E)}\ 75\%</math> | \textbf{(E)}\ 75\%</math> | ||
| + | |||
| + | ==Solution== | ||
| + | Without loss of generality, we can set the list price equal to <math>100</math>. The merchant buys the goods for <math>100*.75=75</math>. Let <math>x</math> be the marked price. | ||
| + | We then use the equation <math>0.8x-75=25</math> to solve for <math>x</math> and get a marked price of <math>\boxed{\textbf{(A)}\ 125\%}</math>. | ||
| + | |||
| + | ==See Also== | ||
| + | {{AHSME 50p box|year=1950|num-b=35|num-a=37}} | ||
| + | |||
| + | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 11:43, 20 September 2024
Problem
A merchant buys goods at 
off the list price. He desires to mark the goods so that he can give a discount of 
on the marked price and still clear a profit of on the selling price. What percent of the list price must he mark the goods?
Solution
Without loss of generality, we can set the list price equal to 
. The merchant buys the goods for 
. Let 
be the marked price.
We then use the equation 
to solve for and get a marked price of 
.
See Also
| 1950 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 35 |
Followed by Problem 37 | |
| 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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
