Question
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
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Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
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.
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.
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