Question

For a certain milk shake recipe, the number of scoops of powder varies

directly with the number of cups of milk. 3 scoops of powder are
needed for 5 cups of milk. What is the formula for the number of
scoops of powder, p, as a function of the number of cups of milk, m?

Answer 1

We know that the number of scoops of powder varies directly with the number of cups of milk. This means that there is a constant ratio between the two quantities.

Let's call this constant ratio k. Then, we can set up a proportion:

scoops of powder / cups of milk = k

We also know that 3 scoops of powder are needed for 5 cups of milk. We can use this information to find k:

3 / 5 = k

Simplifying this gives us:

k = 0.6

Now that we know k, we can use the proportion we set up earlier to find the formula for the number of scoops of powder, p, as a function of the number of cups of milk, m:

p / m = k

Multiplying both sides by m gives us:

p = km

Substituting the value of k we found earlier gives us:

p = 0.6m

Therefore, the formula for the number of scoops of powder, p, as a function of the number of cups of milk, m, is:

p = 0.6m