A beverage company makes 100% cranapplejuice, which is made up of 3 1/4 parts of
cranberry juice to 5 3/4 parts of apple juice, with no other ingredients. How much apple
juice is there in a 64-fluid ounce bottle of cranapplejuice?
cranberry : apple = 3.25 : 5.75
= 325 : 575
= 13 : 23
so 23/36 of 64 fl ounces is apple juice
= 40 8/9 1/9 or appr 40.9 fl ounces
To find out how much apple juice is in a 64-fluid ounce bottle of cranapple juice, we need to determine the ratio of cranberry juice to apple juice and then apply that ratio to the total volume.
From the given information, we know that cranapple juice is composed of 3 1/4 parts of cranberry juice to 5 3/4 parts of apple juice. Let's convert these mixed fractions into improper fractions for easier calculations.
3 1/4 = (4*3 + 1)/4 = 13/4
5 3/4 = (4*5 + 3)/4 = 23/4
Now, let's add these fractions together to get the total parts in cranapple juice:
13/4 + 23/4 = 36/4 = 9
This means that in cranapple juice, there are a total of 9 parts, where 5 3/4 parts are apple juice.
To determine the amount of apple juice in a 64-fluid ounce bottle, we will use a proportion.
Let x be the amount (in ounces) of apple juice in a 64-fluid ounce bottle of cranapple juice.
Based on the proportion:
5 3/4 parts of apple juice = x ounces in a 64-fluid ounce bottle
9 parts = 64 fluid ounces (total)
We can set up the following equation:
(5 3/4) / 9 = x / 64
To solve for x, we can cross-multiply and then solve for x:
(5 3/4) * 64 = 9x
Converting the mixed fraction to an improper fraction:
(23/4) * 64 = 9x
Multiply:
1472/4 = 9x
Simplify:
368 = 9x
Now, divide both sides of the equation by 9 to solve for x:
x = 368 / 9
Calculating:
x ≈ 40.89
Thus, there are approximately 40.89 fluid ounces of apple juice in a 64-fluid ounce bottle of cranapple juice.
To determine the amount of apple juice in a 64-fluid ounce bottle of cranapple juice, we need to calculate the proportion of apple juice in the mixture.
The total number of parts in the mixture is 3 1/4 + 5 3/4 = 9 parts.
To find the proportion of apple juice, we divide the number of parts of apple juice (5 3/4) by the total number of parts (9):
Proportion of apple juice = 5 3/4 / 9
To simplify this fraction, we need to convert 5 3/4 to an improper fraction:
5 3/4 = (4 * 5 + 3) / 4 = 23 / 4
Now, we can divide 23/4 by 9:
Proportion of apple juice = 23 / 4 / 9
= 23 / 4 * 1 / 9
= 23 / (4 * 9)
= 23 / 36
So, the proportion of apple juice in the mixture is 23/36.
To find the amount of apple juice in a 64-fluid ounce bottle of cranapple juice, we multiply the bottle's volume by the proportion of apple juice:
Amount of apple juice = 64 * (23/36)
= 1472/36
≈ 40.89 fluid ounces
Therefore, there is approximately 40.89 fluid ounces of apple juice in a 64-fluid ounce bottle of cranapple juice.