Question 13·Easy·Ratios, Rates, Proportional Relationships, and Units
A recipe uses cups of flour to make muffins. At this same rate, how many cups of flour are needed to make muffins?
(Express the answer as an integer)
For ratio questions like this, quickly decide between two methods: (1) find a unit rate by dividing to get "per 1" (for example, cups per muffin) and then multiply by the new quantity, or (2) set up a clear proportion with matching units in the same positions (cups over muffins = cups over muffins) and cross-multiply to solve. Always do a quick reasonableness check: if you increase the number of muffins, the amount of flour should also increase, and not by an obviously extreme amount.
Hints
Think about the relationship
You know how many cups of flour are needed for 8 muffins. How can you use this to find how much is needed for a different number of muffins?
Use a unit rate or a proportion
Try either finding how many cups of flour are needed for 1 muffin, or set up a fraction like and solve for .
Check the direction of your ratio
Make sure you are keeping the same order in both ratios: cups over muffins in both fractions, not cups over muffins in one and muffins over cups in the other.
Desmos Guide
Use Desmos to compute the scaled amount
In Desmos, type the expression (2/8)*20 to represent "2 cups for 8 muffins, scaled up to 20 muffins." Use the value that Desmos outputs as the number of cups of flour needed.
Step-by-step Explanation
Understand the ratio given
The recipe says 2 cups of flour makes 8 muffins. This is a ratio of flour to muffins: .
You can think about this as either:
- cups of flour per muffin, or
- muffins per cup of flour.
Either way, the relationship stays the same when you scale up.
Find the rate (cups per muffin) or set up a proportion
Option A: Unit rate
Find cups of flour per muffin:
This means each muffin needs cup of flour.
Option B: Proportion
Let be the cups of flour needed for 20 muffins. Set up:
Then solve this proportion for .
Scale up to 20 muffins and finish the calculation
Using the unit rate from Option A:
- Each muffin needs cup.
- For 20 muffins:
Using the proportion from Option B:
So, you need 5 cups of flour to make 20 muffins at the same rate.