Katrina is making trail mix. She combines 3 1/4 cups of almonds, 2 1/2 cups of pecans, and 1 3/4 cups of dark chocolate chips in a bowl. Katrina then separates the trail mix into individual bags that are 3/4-cup servings. How many individual 3/4-cup bags of trail mix can Katrina make? Enter your response in the box.
bags
7
8
9
4
5
6
1
2
3
0
To find out how many 3/4-cup bags of trail mix Katrina can make, we first need to add up all the ingredients she used:
1. Convert the mixed fractions to improper fractions:
– 3 1/4 cups of almonds = (3 × 4 + 1) / 4 = 13/4 cups
– 2 1/2 cups of pecans = (2 × 2 + 1) / 2 = 5/2 cups = 10/4 cups (to have a common denominator)
– 1 3/4 cups of dark chocolate chips = (1 × 4 + 3) / 4 = 7/4 cups
2. Now add them together:
[
frac{13}{4} + frac{10}{4} + frac{7}{4} = frac{30}{4} = frac{15}{2} text{ cups of trail mix}
]
3. Next, to find out how many 3/4-cup servings fit into 15/2 cups, we divide:
[
frac{15/2}{3/4} = frac{15}{2} times frac{4}{3} = frac{15 times 4}{2 times 3} = frac{60}{6} = 10
]