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# Proportions

## Multiplication to solve for an unknown given two equal ratios.

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Pineapple Frenzy

### Proportions

How do you find the price of some quantity given a rate or proportion? Recall that proportions are two ratios set equal to each other.

Credit: user: Fæ
Source: http://commons.wikimedia.org/wiki/File:Pineapples.jpg

[Figure1]

You are at the grocery store and need to buy 15 pineapples. The price for pineapples is $12 for 4. You make your way over to the check out and-- Oh no! The cash register is broken! Unfortunately, there is no provided rate for individual pineapples and now you must calculate how much money the total of 15 pineapples will cost. The clerk is becoming frantic and does not know what to do in this situation. Luckily, with the help of proportions, or equal ratios, you can solve for the price of 15 pineapples at the rate of 4 for$12!

First we must set up the proportion. Set the two ratios equal to each other, with unknown cost x.

[Figure2]

Your total cost for 15 pineapples will be \$45.

Yay, problem averted! You pay the clerk and go home happily with your 15 pineapples.

### Creative Applications

1. Your friend Andrew would also like to buy pineapples. You have since forgotten the supermarket’s rate for pineapples, but you recall paying 45 dollars for 15 pineapples. How could you give your friend an estimate for the cost of his pineapples?

2. What are some useful applications of proportions in daily life?

3. Can you think of a “proportion” or relation with words that one may use in speech or writing? What is this called?

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