Difference between revisions of "1997 AJHSME Problems/Problem 18"

(Created page with "==Problem== At the grocery store last week, small boxes of facial tissue were priced at 4 boxes for <dollar/>5. This week they are on sale at 5 boxes for <dollar/>4. The perce...")
 
Line 7: Line 7:
 
==Solution==
 
==Solution==
  
Last week, each box was <math>\frac{5}{4} = 1.20</math>
+
Last week, each box was <math>\frac{5}{4} = 1.25</math>
  
 
This week, each box is <math>\frac{4}{5} = 0.80</math>
 
This week, each box is <math>\frac{4}{5} = 0.80</math>
Line 13: Line 13:
 
Percent decrease is given by <math>\frac{X_{old} - X_{new}}{X_{old}} \cdot 100\%</math>
 
Percent decrease is given by <math>\frac{X_{old} - X_{new}}{X_{old}} \cdot 100\%</math>
  
This, the percent decrease is <math>\frac{1.2 - 0.8}{1.2}\cdot 100\% = \frac{1}{3} \cdot 100\% \approx 33.33\%</math>, which is closest to <math>\boxed{B}</math>
+
This, the percent decrease is <math>\frac{1.25 - 0.8}{1.25}\cdot 100\% = \frac{45}{125} \cdot 100\% = 36\%</math>, which is closest to <math>\boxed{B}</math>
  
 
== See also ==
 
== See also ==

Revision as of 04:00, 23 December 2012

Problem

At the grocery store last week, small boxes of facial tissue were priced at 4 boxes for <dollar/>5. This week they are on sale at 5 boxes for <dollar/>4. The percent decrease in the price per box during the sale was closest to

$\text{(A)}\ 30\% \qquad \text{(B)}\ 35\% \qquad \text{(C)}\ 40\% \qquad \text{(D)}\ 45\% \qquad \text{(E)}\ 65\%$

Solution

Last week, each box was $\frac{5}{4} = 1.25$

This week, each box is $\frac{4}{5} = 0.80$

Percent decrease is given by $\frac{X_{old} - X_{new}}{X_{old}} \cdot 100\%$

This, the percent decrease is $\frac{1.25 - 0.8}{1.25}\cdot 100\% = \frac{45}{125} \cdot 100\% = 36\%$, which is closest to $\boxed{B}$

See also

1997 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 17
Followed by
Problem 19
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
Invalid username
Login to AoPS