Difference between revisions of "1998 AJHSME Problems/Problem 20"
Talkinaway (talk | contribs) (→Solution) |
(→Problem) |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | ==Problem | + | ==Problem== |
| − | + | Carpet costs <math>\$21.95</math> per square yard and the padding to put under it costs <math>\$2.55</math> per square yard. Felix plans to install padding and carpet in the region shown in the diagram. What is the cost of the carpet and padding needed to exactly cover the room? | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
==Solution== | ==Solution== | ||
| Line 28: | Line 17: | ||
* [[AJHSME Problems and Solutions]] | * [[AJHSME Problems and Solutions]] | ||
* [[Mathematics competition resources]] | * [[Mathematics competition resources]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 00:00, 5 February 2024
Problem
Carpet costs 
per square yard and the padding to put under it costs 
per square yard. Felix plans to install padding and carpet in the region shown in the diagram. What is the cost of the carpet and padding needed to exactly cover the room?
Solution
After both folds are completed, the square would become a triangle that has an area of 
of the original square.
Since the area is 
square inches for 
of the square, 
square inches is the area of square 
The length of the side of a square that has an area of 
square inches is 
inches.
Each side is 
inches, so the total perimeter is 
See also
| 1998 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 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. 
