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)
To find out how many cups of granola are needed, we need to set up a ratio between nuts and granola.
Let's start by representing the amount of nuts with x and the amount of granola with y.
According to the recipe, the ratio of nuts to granola is 1:2. This can be represented as:
x/y = 1/2
We know that the total amount of trail mix to be made is 12 cups. In other words, x + y equals 12.
x + y = 12
Now, let's use the tape diagram to organize our thinking:
[ x/nuts ] ----- [ y/granola ]
Since we need to find the amount of granola, we want to determine the value of y.
Now, let's use the ratio equation to solve for y:
x/y = 1/2
Cross-multiply:
2x = y
Now, we can substitute the value of y in the other equation:
x + y = 12
x + 2x = 12
3x = 12
Divide both sides by 3:
x = 4
Now, we know that x (the amount of nuts) is 4 cups. To find y (the amount of granola), we substitute x into the equation:
2x = y
2(4) = y
8 = y
Therefore, we would need 8 cups of granola to make 12 cups of trail mix.