Charles mixed pineapple juice and orange juice to make a fruit punch. He made a total of 5 1/2 cups of the mixture and used 2 more cups of orange juice than pineapple juice. How much did he use of each type of juice?
To solve this problem, we can set up a system of equations based on the information given.
Let's represent the amount of pineapple juice Charles used as p, and the amount of orange juice he used as o.
From the information given, we know that the total amount of the mixture is 5 1/2 cups. This can be expressed as:
p + o = 5 1/2
We also know that Charles used 2 more cups of orange juice than pineapple juice. So we can write another equation:
o = p + 2
Now we can solve this system of equations to find the values of p and o.
Substituting the second equation into the first equation, we get:
p + (p + 2) = 5 1/2
Combining like terms, we have:
2p + 2 = 5 1/2
Subtracting 2 from both sides, we get:
2p = 3 1/2
To simplify, we can convert 3 1/2 to an improper fraction:
2p = 7/2
Dividing both sides of the equation by 2, we get:
p = 7/4
Therefore, Charles used 7/4 cups of pineapple juice.
We can now substitute this value back into the second equation to find the amount of orange juice:
o = (7/4) + 2
Simplifying, we have:
o = 15/4
Therefore, Charles used 15/4 cups of orange juice.
Converting the fractions to mixed numbers, we find that Charles used 1 3/4 cups of pineapple juice and 3 3/4 cups of orange juice.