David is making his own strawberry yogurt. In his mixture, the number of strawberries is proportional to the amount of milk in cups david uses 2 1/2cups of milk for every 14 strawberries. If david uses 203 strawberries, how much milk will he need?

To determine the amount of milk that David should be adding, we need to generate and expression that would relate the number of strawberries and the number of cups. From the problem statement, it is said that the number of strawberries is directly proportional to the number of cups of milk. We write it as:

X α Y where X represents the number of strawberries and Y represents the number of cups of milk

To get rid of the proportionality sign, we introduce a proportionality constant k. We calculate this by using the initial conditions given.

X = kY

at X = 14 strawberries Y = 2 1/2 cups of milk = 5/2 cups

14 = k (5/2)

k = 28/5

At X = 203

X = kY

203 = 28/5 (Y)

Y = 145/4 or 36 1/4 cups of milk needed