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Difference between revisions of "2006 AMC 10B Problems/Problem 9"

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== Problem ==
 
== Problem ==
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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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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?  
  
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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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<math> \textbf{(A) } 129\qquad \textbf{(B) } 137\qquad \textbf{(C) } 174\qquad \textbf{(D) } 233\qquad \textbf{(E) } 411 </math>
  
 
== Solution ==
 
== Solution ==
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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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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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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 ==
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[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
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{{MAA Notice}}

Latest revision as of 23:54, 1 April 2023

Problem

Francesca uses $100$ grams of lemon juice, $100$ 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?

$\textbf{(A) } 129\qquad \textbf{(B) } 137\qquad \textbf{(C) } 174\qquad \textbf{(D) } 233\qquad \textbf{(E) } 411$

Solution

The calorie to gram ratio of Francesca's lemonade is $\frac{25+386+0}{100+100+400}=\frac{411\textrm{ calories}}{600\textrm{ grams}}=\frac{137\textrm{ calories}}{200\textrm{ grams}}$

So in $200\textrm{ grams}$ of Francesca's lemonade there are $200\textrm{ grams}\cdot\frac{137\textrm{ calories}}{200\textrm{ grams}}=\boxed{\textbf{(B) }137\textrm{ calories}}.$

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

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