Difference between revisions of "1983 AHSME Problems/Problem 7"
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== Problem== | == Problem== | ||
− | Alice sells an item at | + | Alice sells an item at <math>\$10</math> less than the list price and receives <math>10\%</math> of her selling price as her commission. |
− | Bob sells the same item at | + | Bob sells the same item at <math>\$20</math> less than the list price and receives <math>20\%</math> of his selling price as his commission. |
− | If they both get the same commission, then the list price | + | If they both get the same commission, then the list price is |
− | <math>\textbf{(A) } 20\qquad | + | <math>\textbf{(A) } \$20\qquad |
− | \textbf{(B) } 30\qquad | + | \textbf{(B) } \$30\qquad |
− | \textbf{(C) } 50\qquad | + | \textbf{(C) } \$50\qquad |
− | \textbf{(D) } 70\qquad | + | \textbf{(D) } \$70\qquad |
− | \textbf{(E) } 100 </math> | + | \textbf{(E) } \$100 </math> |
==Solution== | ==Solution== | ||
− | If <math>x</math> is the list price, then <math> | + | If <math>x</math> is the list price, then <math>0.1(x-10)=0.2(x-20)</math>. Solving this equation gives <math>x=30</math>, so the answer is <math>\boxed{\textbf{(B) }\$30}</math>. |
+ | |||
+ | ==See Also== | ||
+ | {{AHSME box|year=1983|num-b=6|num-a=8}} | ||
+ | |||
+ | {{MAA Notice}} |
Latest revision as of 15:01, 2 July 2025
Problem
Alice sells an item at less than the list price and receives
of her selling price as her commission.
Bob sells the same item at
less than the list price and receives
of his selling price as his commission.
If they both get the same commission, then the list price is
Solution
If is the list price, then
. Solving this equation gives
, so the answer is
.
See Also
1983 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
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.