Change the scenario in #3 to be a proportional scenario.
To change the scenario in #3 to be a proportional scenario, you need to adjust the values of the variables to maintain a constant ratio.
Here is the original scenario in #3 for reference:
Scenario #3:
A recipe for pancakes requires 2 cups of flour to make 10 pancakes. How many cups of flour are needed to make 20 pancakes?
To make this scenario proportional, the ratio of cups of flour to the number of pancakes must remain constant.
Let's adjust the scenario to fit a proportional relationship:
Proportional Scenario:
A recipe for pancakes requires 1 cup of flour to make 5 pancakes. How many cups of flour are needed to make 20 pancakes?
In this proportional scenario, the ratio of cups of flour to the number of pancakes remains constant at 1 cup:5 pancakes. Therefore, to make 20 pancakes, 4 cups of flour would be needed (20/5 = 4).
Sure, let's change the scenario in question #3 to a proportional scenario:
Scenario: A bakery sells cakes. The number of cakes sold is directly proportional to the number of hours worked by the baker. When the baker works 6 hours, they can sell 8 cakes.
To solve this proportional scenario, we can set up a proportion using the given information:
Number of cakes sold / Number of hours worked = Constant of variation
Let's use "x" to represent the number of hours and "y" to represent the number of cakes.
We can set up the proportion as follows:
y / x = k
where "k" is the constant of variation. Once we find the value of "k," we can use it to solve other related questions.
Using the given information, we plug in the values:
8 / 6 = k
Simplifying the equation, we have:
k = 4/3
Now that we have the value of "k," we can answer related questions.
For example, if we want to find the number of cakes sold when the baker works 9 hours, we can use the proportion:
y / 9 = 4/3
Simplifying the equation:
3y = 36
Dividing by 3 on both sides:
y = 12
Therefore, when the baker works 9 hours, they can sell 12 cakes.