A fruit drink is 15% white grape juice. Use a system of equations to find the amount of pure white grape juice and the amount of this fruit drink needed to make 27 gallons of a new drink that is 21% white grape juice. Round to the nearest tenth
If you have x gallons of 15% juice, then
.15x + 1.00(27-x) = .21(27)
To solve this problem using a system of equations, let's assume the amount of pure white grape juice needed is x gallons, and the amount of fruit drink needed is y gallons.
We are given that the fruit drink is 15% white grape juice. Therefore, the amount of white grape juice in the fruit drink is 0.15y.
We are also given that the new drink should be 21% white grape juice. Therefore, the total amount of white grape juice in the new drink is 0.21(27) = 5.67 gallons.
Now we can set up the system of equations:
Equation 1: x + y = 27 (since the total volume of the new drink is 27 gallons)
Equation 2: 0.15y + x = 5.67 (since the amount of white grape juice in the fruit drink plus the amount of pure white grape juice should equal 5.67 gallons)
Now we can solve this system of equations to find the values of x and y.
Rearrange Equation 1 to solve for x: x = 27 - y
Substitute the value of x in Equation 2: 0.15y + (27 - y) = 5.67
Simplify the equation: 0.15y + 27 - y = 5.67
Combine like terms: -0.85y + 27 = 5.67
Subtract 27 from both sides: -0.85y = -21.33
Divide by -0.85: y = 25.1
Now substitute the value of y into Equation 1 to solve for x:
x + 25.1 = 27
x = 27 - 25.1
x = 1.9
Therefore, the amount of pure white grape juice needed is approximately 1.9 gallons, and the amount of fruit drink needed is approximately 25.1 gallons.