Difference between revisions of "1986 AJHSME Problems/Problem 15"
(→Solution) |
m (→Problem) |
||
| (5 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
| − | Sale prices at the Ajax Outlet Store are <math>50\% </math> below original prices. On Saturdays an additional discount of <math>20\% </math> off the sale price is given. What is the Saturday price of a coat whose original price is | + | Sale prices at the Ajax Outlet Store are <math>50\% </math> below original prices. On Saturdays an additional discount of <math>20\% </math> off the sale price is given. What is the Saturday price of a coat whose original price is <math>\textdollar 180</math>? |
| − | <math>\text{(A)}</math | + | <math>\text{(A)}</math> <math>\textdollar 54</math> |
| − | <math>\text{(B)}</math | + | <math>\text{(B)}</math> <math>\textdollar 72</math> |
| − | <math>\text{(C)}</math | + | <math>\text{(C)}</math> <math>\textdollar 90</math> |
| − | <math>\text{(D)}</math | + | <math>\text{(D)}</math> <math>\textdollar 108</math> |
| − | <math>\text{( | + | <math>\text{(E)}</math> <math>\textdollar 110</math> |
==Solution== | ==Solution== | ||
First we need to do the first discount, which, at Ajax Outlet Store, would be there any day of the week. | First we need to do the first discount, which, at Ajax Outlet Store, would be there any day of the week. | ||
| + | <cmath>\begin{align*} | ||
| + | 180 \times 50\% &= 180 \times \frac{1}{2} \\ | ||
| + | &= 90 \\ | ||
| + | \end{align*}</cmath> | ||
| − | <math> | + | If we discount <math>20\% </math>, then <math>80 \% </math> will be left, so after the second discount, we get |
| + | <cmath>\begin{align*} | ||
| + | 90 \times 80\% &= 90 \times \frac{8}{10} \\ | ||
| + | &= 9 \times 8 \\ | ||
| + | &= 72 \\ | ||
| + | \end{align*}</cmath> | ||
| − | + | <math>\boxed{\text{B}}</math> | |
| − | |||
| − | |||
| − | |||
| − | |||
==See Also== | ==See Also== | ||
| − | [[ | + | {{AJHSME box|year=1986|num-b=14|num-a=16}} |
| + | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 22:48, 18 November 2024
Problem
Sale prices at the Ajax Outlet Store are 
below original prices. On Saturdays an additional discount of 
off the sale price is given. What is the Saturday price of a coat whose original price is 
?
Solution
First we need to do the first discount, which, at Ajax Outlet Store, would be there any day of the week.
If we discount , then 
will be left, so after the second discount, we get
See Also
| 1986 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 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 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
