Difference between revisions of "2006 AMC 10B Problems/Problem 9"
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== Problem == | == Problem == | ||
| − | Francesca uses 100 grams of lemon | + | Francesca uses <math>100</math> grams of lemon juice, <math>100</math> grams of sugar, and <math>400</math> grams of water to make lemonade. There are <math>25</math> calories in <math>100</math> grams of lemon juice and <math>386</math> calories in <math>100</math> grams of sugar. Water contains no calories. How many calories are in <math>200</math> grams of her lemonade? |
| − | <math> \ | + | <math> \textbf{(A) } 129\qquad \textbf{(B) } 137\qquad \textbf{(C) } 174\qquad \textbf{(D) } 233\qquad \textbf{(E) } 411 </math> |
== 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> | + | 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> |
| − | 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} | + | 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}}=\boxed{\textbf{(B) }137\textrm{ calories}}.</math> |
== See Also == | == See Also == | ||
| − | + | {{AMC10 box|year=2006|ab=B|num-b=8|num-a=10}} | |
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 23:54, 1 April 2023
Problem
Francesca uses 
grams of lemon juice, grams of sugar, and 
grams of water to make lemonade. There are 
calories in grams of lemon juice and 
calories in grams of sugar. Water contains no calories. How many calories are in 
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. 
