Final answer:
The ratio of cups of M&Ms to cups of trail mix is 1:6, after calculating the total amount of trail mix and comparing it to the amount of M&Ms.
Step-by-step explanation:
To find the ratio of cups of M&Ms to cups of trail mix that Joe's mom makes, we need to calculate the total amount of trail mix and compare it to the amount of M&Ms. Joe's mom uses 3/4 cups of peanuts, 1/4 cup of M&Ms, and 1/2 cup of raisins for the trail mix.
First, we add together the amounts of the ingredients to find the total cups of trail mix:
- 3/4 cups (peanuts) + 1/4 cup (M&Ms) + 1/2 cup (raisins) = 1 + 1/2 cups = 1 1/2 cups.
Next, we form the ratio of M&Ms to the total trail mix:
- Ratio = 1/4 cup (M&Ms) : 1 1/2 cups (trail mix)
To simplify this ratio, recall that 1 1/2 cups is the same as 3/2 cups when written as an improper fraction. We then multiply both parts of the ratio by 2 to eliminate the fraction in the denominator:
- Ratio = (1/4 cup * 2) : (3/2 cups * 2) = 1/2 : 3
Therefore, the simplified ratio of M&Ms to the total trail mix is 1:6.