Ratios and Proportions

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Problem 1 Solution

(a) 1.3333333     (b) 2.5 cups mix and 1.875 cups water

      (c) 16.66667 cups mix and 12.5 cups water

Solution Steps for Part (a):

What is the ratio of mix to water in each case?

Answer:

We know from the table that the ratio of mix to water in each case is:

Notice that these ratios all reduce to the same decimal using a calculator, 1.3333333, which we may interpret as 1.3333333 parts mix to one part water ( 1.3333333 : 1 ). Notice that order is important in a ratio; the convention is to put the first quantity -- for us the mix amount -- in the numerator (top of fraction) and the second -- the water -- in the denominator (bottom).

Solution Steps for Part (b):

What quantities of mix and water should be used if we want to make 15 pancakes?

Answer:

There are several ways to figure this answer. Here is how to use a proportion to get it. We know from the first row of the table that the ratio of mix to pancakes is 1 : 6. We can get the amount of mix for 15 pancakes using a proportion:

Notice that we've used x for the unknown amount of mix. Cross multiplying this gives:

15 = 6 x and then dividing both sides by 6: 2.5 = x,

So we need 2.5 cups of mix for 15 pancakes. How much water? Using the ratio we found above for mix to water, 1.3333333, and solving:

1.3333333 x = 2.5

x = 2.5 1.3333333 = 1.875.

So we need 1.875 cups of water.

Solution Steps for Part (c):

What quantities of mix and water should be used if we want to make 100 pancakes?

Answer:

Using the same technique as above: We know from the first row of the table that the ratio of mix to pancakes is 1 : 6. We can get the amount of mix for 100 pancakes using a proportion:

Solving for x gives: 16.666667 = x

So we need 16.666667 cups of mix for 100 pancakes. How much water? Using the ratio we found above for mix to water, 1.3333333, and solving:

1.3333333 x = 16.666667

x = 12.5

So we need 12.5 cups of water.

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