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
Let's represent the cups of granola with a variable x.
According to the given ratio, for every 2 cups of granola, we need 1 cup of nuts.
So, for 12 cups of trail mix, we would need 12/2 = 6 cups of nuts.
Since we know that we need 1 cup of nuts for every 2 cups of granola, we can set up the following proportion:
1/2 = 6/x
By cross-multiplying, we get:
x = 12
Therefore, we would need 12 cups of granola to make 12 cups of trail mix.
To solve this problem, we'll use a tape diagram to organize our thinking. A tape diagram is a visual tool that helps us understand and solve math problems.
Step 1: Draw the tape diagram
Start by drawing a tape diagram with two sections. Label one section for nuts and the other section for granola. Since the recipe calls for 1 cup of nuts for every 2 cups of granola, we can represent this as:
Nuts: 1 cup
Granola: _____
Step 2: Fill in the known information
We know that we want to make 12 cups of trail mix. Since the proportion of nuts to granola is 1:2, we can calculate the amount of granola needed by multiplying 12 by 2:
Granola: 12 x 2 = 24 cups
So, you will need 24 cups of granola to make 12 cups of trail mix.
WRONG
Apologies for the mistake in my previous response. Let's try again.
Based on the given ratio of 1 cup of nuts for every 2 cups of granola, we can set up the following equation:
1/2 = x/12
To solve for x, we can cross-multiply:
2x = 12
Dividing both sides by 2:
x = 6
Therefore, you would need 6 cups of granola to make 12 cups of trail mix.
6 IS WRONG
Apologies for the mistake once again. Let's correct it.
Based on the given ratio of 1 cup of nuts for every 2 cups of granola, we can set up the following equation:
1/2 = x/12
To solve for x, we can cross-multiply:
2x = 12
Dividing both sides by 2:
x = 6
Therefore, you would need 6 cups of granola to make 12 cups of trail mix.
6 IS WRONG 2
Apologies for the repeated mistake. Let's solve the problem correctly.
According to the ratio in the trail mix recipe, we need 1 cup of nuts for every 2 cups of granola.
Let's represent the number of cups of granola needed with the variable x.
Since we want to make 12 cups of trail mix and the ratio is 1:2 (nuts to granola), we can set up the following proportion:
1/2 = x/12
To solve for x, we can cross-multiply:
2x = 12
Dividing both sides by 2:
x = 6
Therefore, you will need 6 cups of granola to make 12 cups of trail mix.
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)
Let's use a tape diagram to solve this problem.
Start by drawing a tape diagram with two sections. Label one section for nuts and the other section for granola. Since the recipe calls for 1 cup of nuts for every 2 cups of granola, we can represent this as:
Nuts: 1 cup
Granola: ___ cups
To find out how many cups of granola we need for 12 cups of trail mix, we need to determine the ratio between nuts and granola.
Since the ratio is 1 cup of nuts for every 2 cups of granola, we can split the Granola section of the tape diagram into 2 parts, each representing 2 cups of granola.
Nuts: 1 cup
Granola: 2 cups | 2 cups | 2 cups | 2 cups | 2 cups | 2 cups
Now we can see that for every 1 cup of nuts (denoted by the 1 cup section in the tape diagram), we need a total of 2 + 2 + 2 + 2 + 2 + 2 = 12 cups of granola.
Therefore, to make 12 cups of trail mix, you will need 12 cups of granola.