Answer:
Use both measuring cups 16 times and then use the [tex]\frac{1}{3}[/tex] 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.
[tex]\frac{1}{3}[/tex] cup = [tex]\frac{4}{12}[/tex] cup
[tex]\frac{1}{4}[/tex] cup = [tex]\frac{3}{12}[/tex] cup
10 cups = [tex]\frac{120}{12}[/tex] 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: [tex]\frac{4}{12}[/tex] + [tex]\frac{3}{12}[/tex] = [tex]\frac{7}{12}[/tex] cup in total
No. of scoops using both cups: [tex]\frac{120}{12}[/tex] ÷ [tex]\frac{7}{12}[/tex] = 16 R [tex]\frac{8}{12}[/tex]
You know that using both cups, you can scoop 16 times with a remainder of [tex]\frac{8}{12}[/tex]. You cannot scoop [tex]\frac{8}{12}[/tex] using both cups without the remaining [tex]\frac{1}{12}[/tex] left to scoop, so you have to use only one cup to scoop. The bigger cup is the [tex]\frac{4}{12}[/tex] cup, so I will use that one to scoop the remaining [tex]\frac{8}{12}[/tex].
No. of scoops using the [tex]\frac{4}{12}[/tex] cup: [tex]\frac{8}{12}[/tex] ÷ [tex]\frac{4}{12}[/tex] = 2
Overall, you will use both cups together for 16 times, then use the [tex]\frac{1}{3}[/tex] cup twice.
