A large glass of juice contains a mix of half mango juice and half pumpkin juice. A smaller glass contains pure pumpkin juice. If the two glasses are combined in a pitcher, the result will be 60% pumpkin juice. The volume of the small glass is 4 ounces; what is the volume of the large glass?
let the volume of the larger glass be x ounces
so volume in the pitcher
= x + 4
so .6(x+4) = 4 + .5x
.6x + 2.4 = 4 + .5x
.1x = 1.6
x = 16 ounces
To solve this problem, we can set up an equation based on the information given. Let's assume the volume of the large glass is x ounces.
According to the problem, the large glass contains a mix of half mango juice and half pumpkin juice. This means that the large glass has an equal amount of mango juice and pumpkin juice. Therefore, the large glass contains x/2 ounces of mango juice and x/2 ounces of pumpkin juice.
The small glass contains pure pumpkin juice, so it contains 4 ounces of pumpkin juice.
When the two glasses are combined in a pitcher, the result is 60% pumpkin juice. This means that the total volume of pumpkin juice in the pitcher is 60% of the total volume of the mixture.
Using this information, we can set up the equation:
(x/2 + 4) / (x + 4) = 0.6
Now, let's solve the equation:
Cross multiplying, we get:
(x/2 + 4) = 0.6(x + 4)
Distribute 0.6 to both terms in the parentheses:
x/2 + 4 = 0.6x + 2.4
Subtract 0.6x from both sides:
x/2 - 0.6x = 2.4 - 4
Combining like terms:
-0.1x = -1.6
Divide both sides by -0.1:
x = -1.6 / -0.1
x = 16
Therefore, the volume of the large glass is 16 ounces.