A company sells a container of trail mix that is 10% candy pieces and another container that is 25% candy pieces.
How many cups of each mixture would be needed to make 18 cups that is 20% candy pieces?
(1 point)
Responses
12 cups of the 10% peanuts and 6 cups of the 25% peanuts
6 cups of the 10% peanuts and 12 cups of the 25% peanuts
9 cups of the 10% peanuts and 9 cups of the 25% peanuts
2 cups of the 10% peanuts and 16 cups of the 25% peanuts
Let's denote the number of cups of the 10% candy mixture as x, and the number of cups of the 25% candy mixture as y.
The total number of cups of the mixture is 18, so we have the equation: x + y = 18.
To determine the percentage of candy pieces in the mixture, we can use the weighted average method. The candy pieces in the 10% mixture are 10% of x cups, and the candy pieces in the 25% mixture are 25% of y cups. The total candy pieces in the mixture is 20% of 18 cups, or 0.2*18 = 3.6 cups.
Therefore, we have the equation: 0.1x + 0.25y = 3.6.
Now we have a system of two equations:
x + y = 18
0.1x + 0.25y = 3.6.
To solve this system, we can use substitution or elimination. Let's solve it using elimination.
Multiply the first equation by 0.1 to match the coefficients of x:
0.1x + 0.1y = 1.8
0.1x + 0.25y = 3.6.
Subtract the first equation from the second equation:
(0.1x + 0.25y) - (0.1x + 0.1y) = 3.6 - 1.8
0.25y - 0.1y = 1.8
0.15y = 1.8
y = 1.8 / 0.15
y = 12.
Substitute this value of y into the first equation to solve for x:
x + 12 = 18
x = 18 - 12
x = 6.
Therefore, 6 cups of the 10% candy mixture and 12 cups of the 25% candy mixture are needed to make 18 cups that is 20% candy pieces.
Answer: 6 cups of the 10% candy mixture and 12 cups of the 25% candy mixture.