Question

1) Sally was making donuts at a restaurant. She can make 30 donuts from 8:15 to 9:00. a. if she starts making donuts at 7:35 how many can she get done before 8:15? Explain your reasoning b. Write an equation to represent how many donuts Sally has left to make if she started counting at 8:15-given she already made donuts from 7:35-8:15. Your equation should be in slope intercept form. Explain your reasoning.

Answer 1

It is a question for linear equation

Let the number of donuts be y and the time be x

Since she can make 30 donuts from 8:15 to 9:00

We will find how many minutes from 8:15 to 9:00

There are 45 minutes from 8:15 to 9:00

Then the first point is (45, 30)

We need to find how many donuts she can make from 7:35 to 8:15

Since there are 25 minutes from 7:35 to 8:00

Since there are 15 minutes from 8:00 to 8:15, then

There are 25 + 15 = 40 minutes from 7:35 to 8:15

By using the proportional way we can find the number of donuts

`(30)/(45)=(x)/(40)`

By using the cross multiplication

`\begin{gathered} x*45=30*40 \\ 45x=1200 \end{gathered}`

Divide both sides by 45

`\begin{gathered} (45x)/(45)=(1200)/(45) \\ x=26.66666 \end{gathered}`

Then she can finish 26 donuts before 8:15

b.

The form of the slope-intercept form is

`y=mx+b`

m is the slope

b is the y-intercept (initial amount)

Since she will start counting from 8:15

Then the initial amount will be the 26 donuts

b = 26

The slope will be the ratio between the number of donuts and the time

`\begin{gathered} m=(30)/(45) \\ m=(2)/(3) \end{gathered}`

The equation is

`y=(2)/(3)x+26`