Question

Prove that your recipe makes exactly 10 cups.

Answer 1

Answer:

Use both measuring cups 16 times and then use the $\frac{1}{3}$ cup to measure twice for exactly 10 cups.

Step-by-step explanation:

When working with fractions, I like to make the denominators the same first.

$\frac{1}{3}$ cup = $\frac{4}{12}$ cup

$\frac{1}{4}$ cup = $\frac{3}{12}$ cup

10 cups = $\frac{120}{12}$ cups

Now, for the most efficient method, it would be reasonable to use both cups so that it is quicker.

1 scoop using both cups: $\frac{4}{12}$ + $\frac{3}{12}$ = $\frac{7}{12}$ cup in total

No. of scoops using both cups: $\frac{120}{12}$ ÷ $\frac{7}{12}$ = 16 R $\frac{8}{12}$

You know that using both cups, you can scoop 16 times with a remainder of $\frac{8}{12}$. You cannot scoop $\frac{8}{12}$ using both cups without the remaining $\frac{1}{12}$ left to scoop, so you have to use only one cup to scoop. The bigger cup is the $\frac{4}{12}$ cup, so I will use that one to scoop the remaining $\frac{8}{12}$.

No. of scoops using the  $\frac{4}{12}$ cup: $\frac{8}{12}$ ÷  $\frac{4}{12}$ = 2

Overall, you will use both cups together for 16 times, then use the $\frac{1}{3}$ cup twice.

Answer 2

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