Difference between revisions of "1997 AHSME Problems/Problem 4"
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If <math>b</math> is <math>25\%</math> larger than <math>c</math>, then <math>b = 125</math>. | If <math>b</math> is <math>25\%</math> larger than <math>c</math>, then <math>b = 125</math>. | ||
− | We see that <math>\frac{a}{b} = \frac{150}{125} = 1.2</math> So, <math>a</math> is <math>20\%</math> bigger than <math>b</math>, and the answer is <math>\boxed{ | + | We see that <math>\frac{a}{b} = \frac{150}{125} = 1.2</math> So, <math>a</math> is <math>20\%</math> bigger than <math>b</math>, and the answer is <math>\boxed{A}</math>. |
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== See also == | == See also == |
Revision as of 16:03, 25 December 2011
Problem
If is larger than , and is larger than , then is what percent larger than ?
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 |