Difference between revisions of "2005 AMC 8 Problems/Problem 11"
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==Problem== | ==Problem== | ||
| − | The sales tax rate in | + | The sales tax rate in Rubenenkoville is 6%. During a sale at the Bergville Coat Closet, the price of a coat is discounted 20% from its $90.00 price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up $90.00 and adds 6% sales tax, then subtracts 20% from this total. Jill rings up $90.00, subtracts 20% of the price, then adds 6% of the discounted price for sales tax. What is Jack's total minus Jill's total? |
| − | <math> \textbf{(A)}\ \textdollar | + | <math> \textbf{(A)}\ -\textdollar 1.06\qquad\textbf{(B)}\ -\textdollar 0.53 \qquad\textbf{(C)}\ \textdollar 0\qquad\textbf{(D)}\ \textdollar 0.53\qquad\textbf{(E)}\ \textdollar 1.06 </math> |
==Solution== | ==Solution== | ||
| − | The price | + | The price Jack rings up is <math>\textdollar{(90.00)(1.06)(0.80)}</math>. The price Jill rings up is <math>\textdollar{(90.00)(0.80)(1.06)}</math>. By the commutative property of multiplication, these quantities are the same, and the difference is <math>\boxed{\textbf{(C)}\ \textdollar 0}</math>. |
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| + | Reminder: Commutative states abc = bac= acb =..... and is the same in any order. This only works for addition and multiplication. | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2005|num-b=10|num-a=12}} | {{AMC8 box|year=2005|num-b=10|num-a=12}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 20:51, 19 January 2024
Problem
The sales tax rate in Rubenenkoville is 6%. During a sale at the Bergville Coat Closet, the price of a coat is discounted 20% from its $90.00 price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up $90.00 and adds 6% sales tax, then subtracts 20% from this total. Jill rings up $90.00, subtracts 20% of the price, then adds 6% of the discounted price for sales tax. What is Jack's total minus Jill's total?
Solution
The price Jack rings up is 
. The price Jill rings up is 
. By the commutative property of multiplication, these quantities are the same, and the difference is 
.
Reminder: Commutative states abc = bac= acb =..... and is the same in any order. This only works for addition and multiplication.
See Also
| 2005 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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. 
