Difference between revisions of "2006 AMC 10B Problems/Problem 9"
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== Problem == | == Problem == | ||
| + | Francesca uses 100 grams of lemon juce, 100 grams of sugar, and 400 grams of water to make lemonade. There are 25 calories in 100 grams of lemon juice and 386 calories in 100 grams of sugar. Water contains no calories. How many calories are in 200 grams of her lemonade? | ||
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| + | <math> \mathrm{(A) \ } 129\qquad \mathrm{(B) \ } 137\qquad \mathrm{(C) \ } 174\qquad \mathrm{(D) \ } 233\qquad \mathrm{(E) \ } 411 </math> | ||
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== Solution == | == Solution == | ||
| + | The calorie to gram ratio of Francesca's lemonade is <math>\frac{25+386+0}{100+100+400}=\frac{411\textrm{ calories}}{600\textrm{ grams}}=\frac{137\textrm{ calories}}{200\textrm{ grams}}</math> | ||
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| + | So in <math>200\textrm{ grams}</math> of Francesca's lemonade there are <math>200\textrm{ grams}\cdot\frac{137\textrm{ calories}}{200\textrm{ grams}}=137\textrm{ calories} \Rightarrow B</math> | ||
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== See Also == | == See Also == | ||
| − | + | {{AMC10 box|year=2006|ab=B|num-b=8|num-a=10}} | |
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| + | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Revision as of 18:29, 23 July 2018
Problem
Francesca uses 100 grams of lemon juce, 100 grams of sugar, and 400 grams of water to make lemonade. There are 25 calories in 100 grams of lemon juice and 386 calories in 100 grams of sugar. Water contains no calories. How many calories are in 200 grams of her lemonade?
Solution
The calorie to gram ratio of Francesca's lemonade is 
So in 
of Francesca's lemonade there are 
See Also
| 2006 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 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 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
