Question

Taj has three scoops for measuring flour. The largest scoop holds 2 1/2 times as much as the smallest one. The middle scoop holds 1 3/4 times as much as the smallest one. What are two different ways in which Taj could measure each of the following?

a) 3 1/4 times as much as the smallest
scoop holds
b) 1/2 as much as the smallest scoop holds

Answer 1

a) `3.25C = 2.5C + 1.75C - C`
Put ONE of A and B into the bowl, and take OUT ONE of C.

b) `0.5C = 2.5C - 2C` "B" is not needed. Put ONE of A into the bowl, and take OUT TWO of C.

Explanation:

First, you can set up all of the measures as related to the smallest one:
`A = 2.5C`; `B = 1.75C`
Or, `C = A/2.5`; `C = B/1.75`. With these we can make the combinations easier. Each combination must be some addition of the available cups:
Desired Volume `= xA + yB + zC` With our derived ratios, this becomes:
Desired Volume `= x(2.5C) + y(1.75C) + zC`

a) `3.25C = 2.5C + 1.75C - C`
Put ONE of A and B into the bowl, and take OUT ONE of C.

b) `0.5C = 2.5C - 2C` "B" is not needed. Put ONE of A into the bowl, and take OUT TWO of C.