Scaling the Trail Mix Recipe
The fifth-grade cooking club is making trail mix for a family night. The recipe for one batch says: 2/3 cup raisins, 1/2 cup almonds, and 1 1/4 cups toasted cereal. The club wants to make 3 batches and mix them in one large bowl. The bowl they have can hold 8 cups total. A parent volunteer says they should first find the total cups for one batch, then multiply by 3. Another volunteer says they can just multiply each ingredient by 3 and add. The club also needs to know whether the mixture will fit in the 8-cup bowl with 1/2 cup of space left for stirring. They must decide whether to use a second bowl. Finally, they want to package the mix into bags that hold 1/4 cup each; how many full bags can they make?
1. Find the total number of cups in 3 batches. Show each step.
Read the worked answer
First find one batch:
2/3 + 1/2 + 1 1/4
Use twelfths: 2/3 = 8/12, 1/2 = 6/12, and 1 1/4 = 1 3/12 = 15/12.
8/12 + 6/12 + 15/12 = 29/12 = 2 5/12 cups for one batch.
For 3 batches: 3 × 29/12 = 87/12 = 7 3/12 = 7 1/4 cups.
The total is 7 1/4 cups.
2. The parent says the total will fit with 1/2 cup space. Is the parent correct? Explain.
Read the worked answer
The bowl holds 8 cups. The mixture is 7 1/4 cups, which is 7.25 cups.
8 − 7 1/4 = 3/4 cup of space.
3/4 cup is greater than 1/2 cup, so the parent is correct: there is enough space. In fact, there is 1/4 cup more than the needed 1/2 cup.
3. How many full 1/4-cup bags can they fill from 7 1/4 cups? Show reasoning.
Read the worked answer
7 1/4 cups = 29/4 cups.
Each bag holds 1/4 cup. Divide:
(29/4) ÷ (1/4) = 29/4 × 4/1 = 29.
They can fill 29 full bags.