Question

Robert is planning to spend the day baking c batches of cookies and b batches of brownies. He would like to maximize the total number of batches, c + b. He can bake a batch of cookies in 12 minutes and a batch of brownies in 30 minutes. Robert wants to spend at most 6 hours baking. He also wants to make sure the number of brownies batches is within 2 of the number of batches of cookies. 

Enter values in the space below to complete an inequality constraint for time (in hours) and two inequality constraints on the relative numbers of cookies and brownie batches. Round any decimals to one decimal place.

Answer 1

do u still need help?

Answer 2

Hello @person321 !

Your math problem requires us to convert the word problem into math before we can solve the math. So let's try to do that first.

First, let's make a math equation to represent the amount of time.
The amount of time to bake "c" batches of cookies = (# of minutes per batch) x (# of batches) = 12 x c = 12c
Similarly for the amount of time to bake "b" batches of brownies = (# of minutes per batch) x (# of batches) = 30 x b = 30b

This is going to look like a format of:
(amount of time to bake cookies) + (amount of time to bake brownies) ≤ (total amount of time)

This person wants the (total amount of time) to be "at most 6 hours" but we can't just put "6" as our number because the other amounts of time are in "minutes".
6 hours * 60 minutes in an hour = 360 minutes

So our first equation becomes:

12c + 30b ≤ 360

Answer 3

We can then make a second sentence out of this part in your problem: "He also wants to make sure the number of brownies batches is within 2 of the number of batches of cookies."

This means that we want to create an inequality equation where the possibility for the "b" number of batches of brownies is between (c - 2) and (c + 2) number of batches of cookies.

This will appear as:
c - 2 ≤ b ≤ c + 2


Therefore you want to solve for the system of inequalities:
12c + 30b = 360
c - 2 ≤ b ≤ c + 2

Answer 4

Making the equations was probably the most difficult part, however, if you are confused on how to solve the system of inequalities, please respond to this post @person321