Maggie is making fruit punch. She uses 2 1/2quarts of grape juice and 1 1/2 quarts of orange juice. 1 quart of grape =$1 less and 1 quart of orange juice. The total cost to make the fruit punch is $12.50 how much is each quart of each juice?
To find out the cost of each quart of grape juice and orange juice, we can set up a system of equations.
Let's assume the cost of one quart of grape juice is x dollars, and the cost of one quart of orange juice is y dollars.
According to the given information, Maggie uses 2 1/2 quarts of grape juice and 1 1/2 quarts of orange juice to make the fruit punch.
Therefore, the total cost of the grape juice is 2 1/2x dollars, and the total cost of the orange juice is 1 1/2y dollars.
The problem states that 1 quart of grape juice costs $1 less than 1 quart of orange juice. This can be expressed as:
x = y - 1
The problem also states that the total cost of making the fruit punch is $12.50. This can be expressed as:
2 1/2x + 1 1/2y = 12.50
Now we have a system of two equations:
x = y - 1
2 1/2x + 1 1/2y = 12.50
To solve this system of equations, we can use substitution or elimination methods. Let's use substitution:
From the first equation, we can express x in terms of y:
x = y - 1
Substitute this expression for x in the second equation:
2 1/2(y - 1) + 1 1/2y = 12.50
Simplify and solve for y:
5/2y - 5/2 + 3/2y = 12.50
8/2y - 5/2 = 12.50
(8y - 5)/2 = 12.50
8y - 5 = 25
8y = 30
y = 3.75
Now that we have the value of y, we can substitute it back into the first equation to find x:
x = y - 1
x = 3.75 - 1
x = 2.75
Therefore, the cost of one quart of grape juice is $2.75, and the cost of one quart of orange juice is $3.75.
To find the cost of each quart of grape juice and orange juice, let's assign variables:
Let's say the cost of 1 quart of grape juice is x dollars.
The cost of 1 quart of orange juice will be (x - 1) dollars since it is 1 dollar less than the cost of grape juice.
Now let's calculate the amount of each juice used:
2 1/2 quarts of grape juice = 2.5x dollars
1 1/2 quarts of orange juice = 1.5(x - 1) dollars
The total cost of making the fruit punch is $12.50, so we can set up the equation:
2.5x + 1.5(x - 1) = 12.50
Simplifying the equation:
2.5x + 1.5x - 1.5 = 12.50
4x - 1.5 = 12.50
4x = 14
x = 3.50
Therefore, the cost of 1 quart of grape juice is $3.50, and the cost of 1 quart of orange juice is ($3.50 - $1) = $2.50.