Name ________________________________ Class Period __________
Date ________________________
1.1.1 Review - Using Graphs and Tables to Solve Problems
Crystal Taylor designs and creates cute costumes for cats. She is conducting market research to determine what price to
charge for her creations.
1. Suppose that a market research study produced the following estimates of cat costumes sales at various prices.
Price per Costume (in $) 1
2
3
4
5
6
7
10
15
Number of Costumes
280
260
240
220
200
180
160
100
0
that will Sell
a. Which variable is the independent?________________________ The dependent?_____________________
b. Plot the (price per costume, number of costumes sold)
y
estimates on the graph.
c. Describe the pattern relating values of those variables
and the way that the relationship is shown in the table
and the graph.
d. Predict the numbers of costumes sold if the price is:
i. $9
ii. $13
iii. $17
x
e. Does the rule 𝑁 = 300 − 20𝑝 produce the same pairs of (price per costumes p, number of costumes sold N) values as
the market research study? Explain how you know.
2. Use the data in #1 relating the price per ticket to number of costumes sold to estimate the income from cat
costumes sales at each of the proposed costume prices.
a. Record those income estimates in a table and plot the (price per costumes, income) estimates on a graph.
Price per costume (in $) 1
2
3
4
5
10
15
Income
b. Which variable is the independent?________________________ The dependent?_____________________
c. Plot the (price per costume, number of costumes sold) estimates on the graph.
y
d. Describe the relationship between cat costume price
and income from costume sales. Explain how the
relationship is shown in the table and the graph of (price
per costumes, income) estimates.
x
e. What do your results in parts a and b suggest about
the costume price that will lead to the maximum income
from cat costumes sales? How is your answer shown in
the table and graph in parts a and b?
3. The Tour de France is the world’s largest annual sporting event starting at the end of June. Cyclists all over the world
come to compete in the race. The entire race covers approximately 3,500 kilometers.
a. The very first Tour de France occurred in 1903 and was won by Maurice Garin with an average speed of 26
km/hr. How long did it take Garin to finish the race?
b. Complete a table to display sample pairs of (average speed, race time) values for completion of the 3,500 km
race.
Average Speed
15
20
25
30
35
40
45
(in km/hr)
Race Time
(in hours)
c. Plot the sample (average speed, race time) data on a graph.
y
d. Describe the relationship between the two variables
from the graph.
e. Write a symbolic rule that shows how to calculate race
time t as a function of average speed s in the Tour de
France race.
f.
x
Lance Armstrong finished first in 2005 with an average
speed of 42 km/hr. Use your rule to calculate
Armstrong’s race time. Show your work.
4) Solve the following equations for the indicated variable.
a) 3x + 6 = 27
b) 8x + 11 = -61
c) 19 – 2x = 5
d) -38 = 4x – 6
e) 2(3x – 9) = -14
f) -4(5x + 7) = -68
g) 6(5x – 2) + 3 = 21
h) 8x + 16 – 3x = 6