Jane's Orange-Pineapple Drink (2)
11) On the following day, Jane had made 64 ounces of her orange-
pineapple drink, which is 25% pineapple juice. After having given 12
ounces of it to her son, who wasn't overly fond of pineapple juice, Jane
thought she'd lessen the pineapple juice to just 15%. To do so, how
many ounces of orange juice will she have to add?
Here are two different ways we can solve this:
0.75(52) + 1.00(x) = 0.85(52 + x)
As you can see in this formula, we are focusing on changing the
75% of orange juice to 85%.
Change the decimal numbers to whole numbers by multiplying by
100:
75(52) + 100(x) = 85(52 + x)
x = ounces of orange juice
The first term multiplies the 52 ounces by 75 (from the percent
of orange juice). The second term adds 100 times the number of
ounces (x) of the pure orange juice. Since it is pure orange juice,
it is 100%. The term to the right of the equal sign is the result
we want to obtain: a drink with 85% orange juice, which will be
the previous 52 ounces, plus the additional ounces of orange juice
added to it; and which will, thus, reduce the amount of pineapple
juice to 15%..
Now let us work out this problem:
75(52) + 100(x) = 85(52 + x)
3,900 + 100x = 4,420 + 85x
100x = 520 + 85x
15x = 520
x = 34.66 (ounces)
Let's double-check this:
Before: After (new mixture)
52 ounces 86.66 ounces (52 + 34.66)
75% orange juice 85% orange juice
25% pineapple juice 15% pineapple juice
39 ounces of orange juice 73.661 ounces of orange juice
13 ounces of pineapple juice 12.999 ounces of pineapple juice
------------------------------ ---------------------------------
52 total ounces 86.660 total ounces
Here's another way we can do it:
If we had a 52-ounce mixture of cleaning fluid and water, which
was 25% cleaning fluid, but wanted to dilute the cleaning fluid
to 15%, we would just add the right amount of water to it. When
we make a reduction in this way, using water, we use 0% to signify
the water, as in the following example, which we will also use
for our orange-pineapple drink solution:
0.25(52) + 0.0(x) = 0.15(52 + x)
Change the decimal numbers to whole numbers by multiplying by
100:
25(52) + 0(x) = 15(52 + x)
x = ounces of orange juice
The first term multitplies 52 ounces with 25 (the percent of the
pineapple juice).
In looking at this above formula, it seeks to solve "x," which
is representing the ounces of orange juice that are needed to
make it a true equation. "How many ounces of orange juice must
I add to the 52-ounce mixture of orange juice and pineapple juice
in order to reduce the 25% of pineapple juice to 15%?"
25(52) + 0(x) = 15(52 + x)
1300 = 780 + 15x
520 = 15x
x = 34.66 (ounces of orange juice)