Solving Problems with Direct Variation:

Question

The amount of lemons used to make lemonade varies directly with how many
gallons are made. It takes 32 lemons to make 4 gallons.
How many lemons will it take to make 17 gallons?

Answer 1

Let's set up a proportion to solve this problem.

We know that it takes 32 lemons to make 4 gallons of lemonade. So the constant of variation (k) is 32/4 = 8 lemons per gallon.

Let x be the number of lemons needed to make 17 gallons of lemonade. We can set up the following proportion:

32 lemons / 4 gallons = x lemons / 17 gallons

32/4 = x/17
8 = x/17

Now, cross multiply to solve for x:

8 * 17 = x
x = 136

Therefore, it will take 136 lemons to make 17 gallons of lemonade.