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 use a tape diagram to solve this problem.
Let's represent 1 cup of nuts as 1 unit and 1 cup of granola as 2 units.
Since we want to make 12 cups of trail mix, we'll need:
12 units of nuts (1 cup of nuts for every 1 unit)
x units of granola (1 cup of granola for every 2 units)
We can set up the equation:
12 = 1x/2
To solve for x, we can multiply both sides of the equation by 2:
24 = 1x
Therefore, we'll need 24 cups of granola to make 12 cups of trail mix.
To determine how many cups of granola will be needed to make 12 cups of trail mix, we can set up a proportion based on the ratio provided in the recipe, which is 1 cup of nuts for every 2 cups of granola.
Let's represent the number of cups of granola needed with the variable "x".
Based on the proportion, we have the following relationship:
1 cup of nuts / 2 cups of granola = 12 cups of nuts / x cups of granola
Next, to solve for "x", we can use cross-multiplication:
1 * x = 2 * 12
Simplifying:
x = 2 * 12
x = 24
Therefore, you will need 24 cups of granola to make 12 cups of trail mix.