CPM Homework Help : CAAC Problem 2-102

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2-102.

Use proportional reasoning to solve the following problems. Homework Help ✎
1. A typical small bag of colored candies has about 135 candies in it, 27 of which are blue. At this rate, how many blue candies would you expect in a pile of 1000 colored candies?
2. Ten calculators cost $149.50. How much would 100 cost? 1000? 500?
3. Tickets to 50 home baseball games would cost $1137.50. How much would it cost to get tickets for all 81 home games? How many games could you go to for $728?

Hint (a):

Use proportions to set up the problem.

$\frac{27\text{ blue}}{135\text{total}} = \frac{n}{1000\text{ total}}$

$27\cdot 1000=135 \cdot n$

$\frac{27000}{135}=\frac{135n}{135}$

Answer (a):

n = 200

Hint (b):

Use proportions to set up the problem.

$\frac{10}{149.50}=\frac{100}{n}$

More Help (b):

Multiply by a fraction equal to 1 in order to make the equivalent proportions have exactly similar numbers.

$\frac{10}{149.50}\cdot \frac{10}{10}=\frac{100}{n}$

Solve for n by multiplying 149.50 by 10.

Answer (b):

n = $1495

Hint (c):

Use the strategy seen in part (a).

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