A company sells a container of trail mix that is 10% candy pieces and another container that is 25% candy pieces.%0AHow many cups of each mixture would be needed to make 18 cups that is 20% candy pieces?%0A(1 point)%0AResponses%0A%0A12 cups of the 10% peanuts and 6 cups of the 25% peanuts%0A12 cups of the 10% peanuts and 6 cups of the 25% peanuts%0A%0A6 cups of the 10% peanuts and 12 cups of the 25% peanuts%0A6 cups of the 10% peanuts and 12 cups of the 25% peanuts%0A%0A9 cups of the 10% peanuts and 9 cups of the 25% peanuts%0A9 cups of the 10% peanuts and 9 cups of the 25% peanuts%0A%0A2 cups of the 10% peanuts and 16 cups of the 25% peanuts
Let's assume that we need x cups of the 10% candy mixture and y cups of the 25% candy mixture to make 18 cups of a 20% candy mixture.
The amount of candy in x cups of the 10% mixture is 0.1x cups.
The amount of candy in y cups of the 25% mixture is 0.25y cups.
The total amount of candy in the 18 cups of the 20% mixture is 0.2(18) = 3.6 cups.
Since the total amount of candy should be the sum of the candy in the two mixtures, we have the equation:
0.1x + 0.25y = 3.6
To solve for x and y, we need another equation. Since we want the total number of cups to be 18, we have:
x + y = 18
To find the values of x and y, we solve this system of equations.
Multiplying the second equation by 0.1, we get:
0.1x + 0.1y = 1.8
Subtracting this equation from the first equation, we eliminate the x terms:
(0.1x + 0.25y) - (0.1x + 0.1y) = 3.6 - 1.8
0.15y = 1.8
y = 1.8 / 0.15
y = 12
Substituting the value of y in the second equation, we get:
x + 12 = 18
x = 18 - 12
x = 6
Therefore, we need 6 cups of the 10% candy mixture and 12 cups of the 25% candy mixture to make 18 cups of a 20% candy mixture.
are you sure? can you explain
Apologies for the confusion. Let's go through the problem step by step.
We need to mix two types of trail mix, one with 10% candy pieces and the other with 25% candy pieces, to create a mixture that is 20% candy pieces.
Let's assume we need x cups of the 10% candy mixture and y cups of the 25% candy mixture to make a total of 18 cups.
The amount of candy in x cups of the 10% mixture is 0.1x cups.
The amount of candy in y cups of the 25% mixture is 0.25y cups.
We are trying to find the values of x and y such that when combined, the total candy amount in the mixture is 20% of 18 cups.
First, let's set up the equation for the total candy amount:
0.1x + 0.25y = 0.2 * 18
0.1x + 0.25y = 3.6
Next, we need another equation to solve for x and y. Since the total number of cups in the mixture is 18, we have:
x + y = 18
Now we have a system of two equations:
0.1x + 0.25y = 3.6
x + y = 18
We can solve this system of equations to find the values of x and y.
Multiplying the second equation by 0.1, we get:
0.1x + 0.1y = 1.8
Subtracting this equation from the first equation, we eliminate the x terms:
(0.1x + 0.25y) - (0.1x + 0.1y) = 3.6 - 1.8
0.15y = 1.8
y = 1.8 / 0.15
y = 12
Substituting the value of y in the second equation, we get:
x + 12 = 18
x = 18 - 12
x = 6
Therefore, the correct answer is 6 cups of the 10% candy mixture and 12 cups of the 25% candy mixture to make 18 cups of a 20% candy mixture.