Draw a graph where the axes represent the number of bracelets made and time in minutes.
See solution.
Practice makes perfect
We are asked to draw a graph illustrating the information given in the question.
There are two parts of this information.
A limit is given on the time Payton spends on making the jewelry on Saturdays.
It is given how long it takes for her to make the bracelets.
To illustrate these on a graph, let's introduce variables n for the number of bracelets Payton makes and t for the time she spends on making the bracelets.
Upper Bound on the Time Spent
It is given that Payton spends no more than 3 hours on making jewelry. Let's convert this time to minutes and write an inequality.
t≤ 3* 60=180
The region illustrating this inequality is the half plane below the line t=180.
Time Needed to Make the Bracelets
It is given that Payton needs 15 minutes to set up her supplies and an additional 25 minutes to make each bracelet. She may use more time, so the following inequality gives the time she uses to make n bracelets.
t≥ 15+25n
The graph of this inequality is a half plane bounded by the line we get by replacing the inequality symbol with an equals sign.
t= 15+25n
We can draw this boundary line through any two of the points.
Number of Bracelets
Time Needed
Point on Line
1
15+25(1)=40 minutes
(1,40)
2
15+25(2)=65 minutes
(1,65)
Let's graph these points and draw the line through them.
To decide which half plane to shade, we use a test point. Since 0 minutes is not enough to make 1 bracelet, the point (1,0) is not in the shaded region.
Putting the Graphs Together
Let's draw the two graphs on the same coordinate plane. Let's also include a third half plane that indicates that the number of bracelets Payton makes is not negative.
n≥ 0
The common part of the shaded half planes represents the conditions given in the question.
This shaded area represents the possible number of bracelets that Payton can make within a given time frame. For example, point (2,120) is in the shaded region. It represents Payton making 2 bracelets and it taking her 120 minutes to make them.
Extra
Alternative Interpretation
The question can also be understood in a way that Payton uses exactly 15 minutes to set up her supplies and 25 minutes to make each bracelet. In this case, the time used to make n bracelets is exactly t=15+25n. The following diagram represents this situation.
Since Payton can only make a whole number of bracelets, the yellow dots show that in 3 hours she can make at most 6 bracelets.
