Difference between revisions of "1997 AHSME Problems/Problem 4"
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<math> \mathrm{(A)\ } 20\% \qquad \mathrm{(B) \ }25\% \qquad \mathrm{(C) \ } 50\% \qquad \mathrm{(D) \ } 100\% \qquad \mathrm{(E) \ }200\% </math> | <math> \mathrm{(A)\ } 20\% \qquad \mathrm{(B) \ }25\% \qquad \mathrm{(C) \ } 50\% \qquad \mathrm{(D) \ } 100\% \qquad \mathrm{(E) \ }200\% </math> | ||
− | ==Solution 1== | + | __TOC__ |
+ | == Solution == | ||
+ | ===Solution 1=== | ||
Translating each sentence into an equation, <math>a = 1.5c</math> and <math>b = 1.25c</math>. | Translating each sentence into an equation, <math>a = 1.5c</math> and <math>b = 1.25c</math>. | ||
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In this case, <math>a</math> is <math>1.2 - 1 = 0.2 = 20\%</math> bigger than <math>b</math>, and the answer is <math>\boxed{B}</math>. | In this case, <math>a</math> is <math>1.2 - 1 = 0.2 = 20\%</math> bigger than <math>b</math>, and the answer is <math>\boxed{B}</math>. | ||
− | ==Solution 2== | + | ===Solution 2=== |
Arbitrarily assign a value to one of the variables. Since <math>c</math> is the smallest variable, let <math>c = 100</math>. | Arbitrarily assign a value to one of the variables. Since <math>c</math> is the smallest variable, let <math>c = 100</math>. | ||
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== See also == | == See also == | ||
{{AHSME box|year=1997|num-b=3|num-a=5}} | {{AHSME box|year=1997|num-b=3|num-a=5}} | ||
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+ | [[Category:Introductory Algebra Problems]] |
Revision as of 18:27, 9 August 2011
Problem
If is larger than , and is larger than , then is what percent larger than ?
Contents
[hide]Solution
Solution 1
Translating each sentence into an equation, and .
We want a relationship between and . Dividing the second equation into the first will cancel the , so we try that and get:
In this case, is bigger than , and the answer is .
Solution 2
Arbitrarily assign a value to one of the variables. Since is the smallest variable, let .
If is larger than , then .
If is larger than , then .
We see that So, is bigger than , and the answer is .
See also
1997 AHSME (Problems • Answer Key • Resources) | ||
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |