Whitney baked 40 cookies with 4 scoops of flour. How many scoops of flour does Whitney need in order to bake 80 cookies, assuming a direct proportional relationship?
Understand the Problem
The question is asking us to determine the amount of flour needed to bake 80 cookies, given that 4 scoops of flour are needed for 40 cookies and the variables are directly proportional. We must determine the ratio of cookies to flour and use it to determine the amount of flour needed for 80 cookies.
Answer
8 scoops of flour.
Answer for screen readers
8 scoops of flour are needed to bake 80 cookies.
Steps to Solve
- Determine the ratio of flour scoops to cookies.
We are given that 4 scoops of flour are needed for 40 cookies. We can express this as a ratio:
$\frac{4 \text{ scoops}}{40 \text{ cookies}}$
- Simplify the ratio.
We simplify the ratio to find the amount of scoops needed for 1 cookie:
$\frac{4}{40} = \frac{1}{10}$
This means $\frac{1}{10}$ of a scoop of flour is needed for each cookie.
- Calculate the amount of flour needed for 80 cookies.
Multiply the simplified ratio by the desired number of cookies (80):
$\frac{1}{10} \frac{\text{scoop}}{\text{cookie}} \times 80 \text{ cookies} = \frac{80}{10} \text{ scoops}$
$\frac{80}{10} = 8$
Therefore, 8 scoops of flour are needed for 80 cookies.
8 scoops of flour are needed to bake 80 cookies.
More Information
This is a direct proportion problem because as the number of cookies increases, the amount of flour needed also increases proportionally.
Tips
A common mistake is to set up the proportion incorrectly. For example, some might incorrectly assume the ratio of cookies to scoops of flour. Also, not simplifying the fraction can lead to larger numbers and potential calculation errors.
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