A trail mix recipe calls for 1 cup of nuts for every 2 cups of granola. If you want to make 12 cups of trail mix, how many cups of granola will you need? Use a tape diagram to help organize your thinking.(1 point)
cups and it's not 24 or 12
To find the number of cups of granola needed, we can use the ratio of 1 cup of nuts to 2 cups of granola.
Let's represent the number of cups of nuts as "N" and the number of cups of granola as "G".
Since the ratio of nuts to granola is 1:2, we can set up the following equation:
Nuts/Granola = 1/2
We know that the total amount of trail mix we want to make is 12 cups. This can be represented as:
Total Trail Mix = N + G = 12
By substituting N = 1/2 * G into the equation, we can solve for G:
1/2 * G + G = 12
3/2 * G = 12
Multiplying both sides by 2/3:
G = 12 * 2/3
G = 8
Therefore, you will need 8 cups of granola for 12 cups of trail mix.
To figure out how many cups of granola you will need, we can use a tape diagram.
The recipe states that for every 1 cup of nuts, we need 2 cups of granola. Let's represent 1 cup of nuts with a square and 2 cups of granola with a rectangle.
Using the given information, we can create the tape diagram as follows:
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| |
|___|
This represents 1 cup of nuts.
Now, we need to determine how many cups of granola will be needed for 12 cups of trail mix.
Since we have 12 cups of trail mix, we will need 12 squares to represent the cups of nuts.
| | | | | | | | | | | | |
| | | | | | | | | | | | |
|___|___|___|___|___|___|___|___|___|___|___|___|
Now, we can determine the number of rectangles needed to represent the cups of granola.
Since we have 12 squares (cups of nuts), we will need twice as many rectangles (cups of granola).
Therefore, we will need:
12 x 2 = 24 cups of granola.
Hence, to make 12 cups of trail mix, you will need 24 cups of granola.
To solve this problem using a tape diagram:
Let's represent the cups of nuts and granola with two separate sections of the tape diagram. Since the ratio of nuts to granola is 1:2, we can divide each section of the tape diagram into equal parts.
Since we want to make 12 cups of trail mix, let's represent this amount on the tape diagram.
Here is the tape diagram representation:
Nuts: 1 cup of nuts
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Granola: 2 cups of granola
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Since the tape diagram representation shows that for every 1 cup of nuts, we need 2 cups of granola, we can scale up the diagram until we reach 12 cups of trail mix.
Nuts: (1 cup of nuts) x (12 cups of trail mix / 1 cup of nuts)
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Granola: (2 cups of granola) x (12 cups of trail mix / 1 cup of nuts)
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Simplifying the expression, we have:
Nuts: (1 x 12) cups = 12 cups
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Granola: (2 x 12) cups = 24 cups
Therefore, to make 12 cups of trail mix, you will need 24 cups of granola.