Difference between revisions of "2012 AMC 12B Problems/Problem 4"
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==Solution== | ==Solution== | ||
− | The ratio <math>\frac{400 \text{ euros}}{500 \text{ dollars}}</math> can be simplified using | + | The ratio <math>\frac{400 \text{ euros}}{500 \text{ dollars}}</math> can be simplified using conversion factors:<cmath>\frac{400 \text{ euros}}{500 \text{ dollars}} \cdot \frac{1.3 \text{ dollars}}{1 \text{ euro}} = \frac{520}{500} = 1.04</cmath> which means the money is greater by <math>\boxed{ \textbf{(B)} \ 4 }</math> percent. |
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+ | ==Solution 2== | ||
+ | If we divide each of Etienne's and Diana's values by <math>100</math>, the problem stays the same. Then, Etienne has <math>1.3</math> times the amount of money Diana has, so Etienne has <math>5.2</math> dollars. Since <math>\dfrac{5.2}{5} = 1.04</math>, Etienne has <math>\boxed{ \textbf{(B)} \ 4 }</math> percent more money than Diana. ~Extremelysupercooldude | ||
== See Also == | == See Also == |
Latest revision as of 06:18, 29 June 2023
Contents
Problem
Suppose that the euro is worth 1.3 dollars. If Diana has 500 dollars and Etienne has 400 euros, by what percent is the value of Etienne's money greater that the value of Diana's money?
Solution
The ratio can be simplified using conversion factors: which means the money is greater by percent.
Solution 2
If we divide each of Etienne's and Diana's values by , the problem stays the same. Then, Etienne has times the amount of money Diana has, so Etienne has dollars. Since , Etienne has percent more money than Diana. ~Extremelysupercooldude
See Also
2012 AMC 12B (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 | |
All AMC 12 Problems and Solutions |
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