2006 AMC 10B Problem 9

Question

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?

129

137

174

223

411

The whole batch weighs

600

grams and holds

25+386

calories

Scale the total calories by

\tfrac{200}{600}

The lemonade totals

100+100+400=600

grams containing

25+386=411

calories.

In

200

grams there are

411\cdot\tfrac{200}{600}=\tfrac{411}{3}=137

calories.

Thus, the correct answer is B.

Problem 9 in other years