2006 AMC 10B Problems/Problem 9

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 (ProblemsAnswer KeyResources)
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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