A cookie recipe uses 3 cups of flour to make 24 cookies. Using the same ratio of flour to cookies, how many cups of flour are needed to make 40 cookies?
For ratio questions like this, quickly decide whether to use a unit rate or a proportion. A fast method is to find the unit rate (amount per 1 item), then multiply by the desired number; here, compute cups per cookie, then multiply by the new cookie count. Alternatively, set up a proportion with matching units across numerators and denominators (cups over cookies equals cups over cookies), solve for the unknown, and always double-check that your answer makes sense (more cookies should require more flour, and roughly in the same scale).
Hints
Think about the relationship
If 3 cups of flour make 24 cookies, what happens to the amount of flour if you make more cookies but keep the same recipe?
Use a unit rate or proportion
Try either finding how many cups of flour are needed for 1 cookie, or set up a proportion like .
Check the scaling factor
From 24 cookies to 40 cookies, by what factor are you multiplying the number of cookies? Use that same factor on the cups of flour, or use your unit rate to multiply by 40.
Desmos Guide
Use Desmos to apply the ratio
In Desmos, type 3/24 * 40 and look at the value it returns. That value is the number of cups of flour needed for 40 cookies using the same recipe ratio.
Step-by-step Explanation
Understand the proportional relationship
The recipe uses 3 cups of flour for 24 cookies. This means the ratio of flour to cookies must stay the same when you change the number of cookies. So whatever you do to the cookies, you must do proportionally to the cups of flour.
Find flour per cookie (unit rate)
Compute how many cups of flour are used for 1 cookie.
So each cookie needs cup of flour.
Scale up to 40 cookies
Now multiply the flour needed for 1 cookie by 40 to get the flour for 40 cookies.
So the number of cups of flour needed to make 40 cookies is 5, which corresponds to choice B.