Examples: Applications Using Proportions


>>We want to solve the following
problem using a proportion. A basketball player makes
17 out of 20 free throws. If he shoots 150 free throws, how
many can you expect him to make? So we’ll set up two ratios
comparing the successful free throws to the total number of attempts. So from this first sentence, we know
he made 17 free throws out of 20, so we’re comparing successful free
throws to the number of attempts. So this must equal the ratio of
x to 150 where x is the number of successful free throws out of 150 attempts. And now we can cross multiply and solve for
x. Twenty times x must equal 17 times 150. So we have 20 x must equal 17
times 150, is equal to 2,550. And now we’ll divide both sides by 20 to
solve for x. So x is equal to this quotient. Let’s go ahead and use the calculator. 2,550 divided by 20, so x is equal to 127.5. Now, there’s a little bit of a problem with
this answer because this represents the number of successful free throws out of 150. It’s not possible to make half of a free throw. So if we round this to the nearest whole number,
we can say that x is approximately equal to 128 or rounded to the nearest free throw, we expect him to make 128 free
throws out of the next 150 attempts. Let’s take a look at another example. Here we’re given a scale on a map indicates
3/4 of an inch represents 40 miles. If two cities are 4 inches apart
on the map, how far apart are they? So we’ll set up two ratios comparing the length
on the map to the actual length in miles. So our first ratio will be 3/4 to 40. Notice how we’re comparing the number of inches
on the map to the actual distance in miles. So we must keep this consistent. So for the second ratio, the 4
inches is the length on the map. So we’ll have the ratio of 4 to x where x
represents the actual distance in miles. So 3/4 times x must equal 40 times 4. And 40 times 4 is equal to 160. And now to solve for x, we’ll
multiply both sides of the equation by the reciprocal of 3/4, which will be 4/3. Let’s go ahead and put 160 over 1. So on the left side everything
simplifies out, we’re left with x. And on the right side we have 4/3 times 160. Three and 160 do not share a
common factor, so we’ll go ahead and multiply our numerator
and denominator together. Four times 160 is going to be 640. Our denominator is 3. So let’s go back to the calculator,
640 divided by three. So x is equal to 213.3 repeating. We should recognize this decimal as 1/3. So x is 213 and 1/3 miles, which would
be the distance between the two cities that are 4 inches apart on the map. Let’s take a look at one more. An ice cream label states that one
6 ounce serving has 8 grams of fat. If a container contains 20 ounces, how
much fat is in the entire container. So we’ll set up two ratios comparing the
number of ounces to the number of fat grams. So a 6 ounce serving has 8 grams of fat,
and the second ratio will be 20 ounces to an unknown number of fat grams. So now we can cross multiply and solve
for x. Six times x must equal 8 times 20. So we have 6 x equals 8 times
20 is equal to 160. And we’ll divide both sides by 6 to determine
how many fat grams we’d have in 20 ounces. So if x equals 160 divided by 6, so this
would be 26.6 repeating, or 26 and 2/3 grams of fat in 20 ounces of ice cream.
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