A bakery recipe uses exactly 3 cups of sugar to bake 60 cookies.
Using the same recipe, how many cups of sugar are needed to bake 150 cookies?
For ratio and proportion questions like this, quickly recognize that the relationship is linear: doubling the cookies doubles the sugar, tripling the cookies triples the sugar, and so on. The fastest methods are either (1) find the unit rate by dividing (e.g., cups per cookie) and then multiply by the desired quantity, or (2) set up a proportion like and solve for . Always keep units in mind (cups vs. cookies) to avoid mixing quantities and to check that your final result has the correct unit.
Hints
Think about proportional relationships
If 3 cups of sugar make 60 cookies, what happens to the amount of sugar if you make more cookies using the same recipe? The ratio must stay the same.
Find the sugar for one cookie first
Try to find how many cups of sugar are needed for 1 cookie by dividing 3 cups by 60 cookies.
Scale up to 150 cookies
Once you know the sugar needed for 1 cookie, multiply that amount by 150 to find the total sugar for 150 cookies.
Desmos Guide
Use Desmos to compute the proportional amount
In the expression line, type 3/60*150 and press Enter. The numerical result shown is the number of cups of sugar needed for 150 cookies.
Step-by-step Explanation
Understand the proportional relationship
The recipe is the same no matter how many cookies you bake, so the ratio of sugar to cookies stays constant.
Originally, the recipe uses 3 cups of sugar for 60 cookies. This means the amount of sugar is directly proportional to the number of cookies.
Find the sugar per cookie (unit rate)
Compute how many cups of sugar are used for 1 cookie.
- Sugar per cookie
- Simplify:
So the recipe uses cup of sugar for each cookie.
Scale up to 150 cookies and compute the total sugar
Now multiply the sugar per cookie by 150 cookies:
- Total sugar cups
So, you need 7.5 cups of sugar to bake 150 cookies.