Proportions problem

Question

Your father is planning to cook for 20 people using a recipe that specifies one and a fourth cups of sugar for every six people.

For the larger group, your father will require how many cups of sugar.

Hint: Write a proportion for the phrase. Then, solve for the larger number of cups of sugar needed.

Answer 1

We know that the larger group is 20 people, and we want to solve for how many cups of sugar to use. Since we're solving for how many cups of sugar, we can use a variable to represent that amount. Cups of sugar needed = s.

We also know that for 6 people, we need 1 and a fourth cups, which we can also write as 1.25 cups.

There are different ways to set up the proportion equation, but the important thing is to make sure it follows the same pattern on both sides. For example, we could do people divided by cups, cups divided by people, larger group divided by smaller group... as long as it is the same pattern on both sides, we will still get the correct answer.

Let's do cups divided by people. For the smaller group, we have 1.25 cups and 6 people, so we get 1.25/6. On the other side of the equation, for the larger group, we have s cups and 20 people, so we get s/20.

1.25/6 = s/20

multiply both sides by 20

25/6 = s

So we need 25/6 cups of sugar for 20 people. We can also write 25/6 as 4 and one sixth.