Difference between revisions of "2006 AMC 12B Problems/Problem 4"

(Alternative Solution)
(Alternative Solution)
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So <math> 20 - (8+5+3+2+1) = 1 </math>
 
So <math> 20 - (8+5+3+2+1) = 1 </math>
<math> 20* \frac{x}{100}=1 </math>
 
  
By simplifying to "x", we get <math>5</math>
+
We can make an equation: <math> 20* \frac{x}{100}=1 </math>
 +
 
 +
If we simplify the equation to "x", we get <math>5</math>
  
 
== See also ==
 
== See also ==
 
{{AMC12 box|year=2006|ab=B|num-b=3|num-a=5}}
 
{{AMC12 box|year=2006|ab=B|num-b=3|num-a=5}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 20:06, 26 July 2013

Problem

Mary is about to pay for five items at the grocery store. The prices of the items are $&#036;$7.99$,$$ $4.99$, $&#036;$2.99$,$$ $1.99$, and $&#036;$0.99$.  Mary will pay with a twenty-dollar bill.  Which of the following is closest to the percentage of the$$ $20.00$ that she will receive in change?

$\text {(A) } 5 \qquad \text {(B) } 10 \qquad \text {(C) } 15 \qquad \text {(D) } 20 \qquad \text {(E) } 25$

Solution

The total price of the items is $(8-.01)+(5-.01)+(3-.01)+(2-.01)+(1-.01)=19-.05=18.95$

$20-18.95=1.05$

$\frac{1.05}{20}=.0525 \Rightarrow \text{(A)}$

Alternative Solution

We can round the prices to $8$, $5$, $3$, $2$, and $1$.

So $20 - (8+5+3+2+1) = 1$

We can make an equation: $20* \frac{x}{100}=1$

If we simplify the equation to "x", we get $5$

See also

2006 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
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 AMC 12 Problems and Solutions

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