A recipe uses 1/3 cup of brown sugar to make 18 cookies. How many cups of brown sugar are need to make 45 cookies? Explain.

x/45 = (1/3)/18

x/45 = 1/54
Now solve for x

To find out how many cups of brown sugar are needed to make 45 cookies, we can set up a proportion based on the number of cookies and the amount of brown sugar needed:

Number of cookies / Amount of brown sugar = Number of cookies / Amount of brown sugar

In this case, the original recipe uses 18 cookies and 1/3 cup of brown sugar, so we have:

18 cookies / 1/3 cup = 45 cookies / x cups

To solve for x, we can cross-multiply:

18 * x cups = 45 * 1/3

18x = 15

Next, we divide both sides of the equation by 18 to isolate x:

x = 15 / 18

Simplifying the right side gives:

x = 5 / 6

Therefore, to make 45 cookies, you would need 5/6 (or approximately 0.833) cups of brown sugar.

To find out how many cups of brown sugar are needed to make 45 cookies, we can use a proportional relationship.

First, let's calculate the amount of brown sugar needed for one cookie. Since the recipe uses 1/3 cup of brown sugar to make 18 cookies, we can divide 1/3 by 18 to find the amount of brown sugar needed for one cookie.

1/3 cup / 18 cookies = 1/54 cup of brown sugar per cookie

Now, knowing the amount of brown sugar needed for one cookie, we can multiply it by the number of cookies we want to make, which is 45.

1/54 cup per cookie * 45 cookies = 45/54 cup of brown sugar

To simplify the fraction, we divide both the numerator and denominator by their greatest common divisor, which in this case is 9:

45/54 cup of brown sugar = (45 ÷ 9) / (54 ÷ 9) cup of brown sugar = 5/6 cup of brown sugar

Therefore, to make 45 cookies, you will need 5/6 cup (or 0.83 cup) of brown sugar.