Math 2201 Chapter 8 Assignment Solutions
Name _________________________________________
Answer all questions on this sheet and show all workings for full credit.
1. In the month of May, Jessica sent 4216 text messages. During a one-week period, Patrick sent 1008
texts. Who has the higher text rate per day?
Assuming 31 days in the month,
Jessica
4216
31
136txts/day
Patrick
1008
7
144txts/day
Patrick had the higher text rate per day
2.
Paper towels are sold in a 2-roll package for $2.49 and a 12-roll package for $12.99.
a) What package has the lower unit price?
2-pk roll
2.49
2
$1.25/roll
12-pk roll
12.99
12
$1.08/roll
The 12-roll pack has the lower unit price.
b) How much would you save by buying a 12-roll package rather than six 2-roll packages?
6  2.49  $14.94
14.94  12.99  $1.95
You would save $1.95
c) When deciding which package size is the better buy for you, what should you consider in
addition to unit price?
Size (storage space), strength, size of sheet, etc.
3. (OMIT) Sean buys a package of 15 pencils for $4.50 at Walmart. Angela buys a box of 50 pencils
at Costco for $14.00. Which is the better buy?
4.
Each of your finger nails grow at about 0.05 cm/week. Each of your toe nails grow at about 0.65
cm/year. Do your toe nails or finger nails grow faster?
Finger Nails
Toe Nails
0.05  52  2.6cm/yr
0.65cm/yr
Your finger nails grow faster.
5. The graph below shows the population (in thousands) in Newfoundland from 1956 to 2006.
a) What does a positive slope indicate in this graph?
An increasing population
b) What does a negative slope indicate in this graph?
A decreasing population
c) What does the slope of a horizontal line indicate in this graph?
A stable population
d) What does the steepness of the slope represent in this graph?
The rate at which the population is increasing or decreasing.
6. The following table represents the average cost per litre of regular gasoline in Newfoundland and
Labrador for the first six months of 2011.
Month
Cost (cents/L)
January(1) February(2)
121.2
123.6
March(3)
131.4
April(4)
139.2
May(5)
133.1
June(6)
131.9
Using a graph, determine between which months the cost per litre of gas decreased the least amount.
Give reasons why you think this occurred.
The cost of gas decreased the least amount from May to June. The line segment joining the
prices for May & June has a negative slope  m  1.2cents/L  but the segment is not as steep as the
segment joining April to May  m  6.1cents/L  . This occurred because the demand for gas decreased
during these times.
7. (OMIT) During a Terry Fox Run, student volunteers distribute 250 mL cups of water to
participants as they cross the finish line. Each volunteer has a cooler that can hold 64 L of water.
How many cups of water can each volunteer dispense?
8. (OMIT) Loose-leaf paper costs $1.49 for 200 sheets or $3.49 for 500 sheets. What is the least
you can pay for 100 sheets? 1600 sheets?
9. (OMIT) Betty earns $463.25 in 5 weeks. How much will she earn in 2 years?
10. The average monthly temperature in Corner Brook, NL, in °C, is recorded in the chart below.
The sampling period for this data covers 30 years.
Month
January(1)
February(2)
March(3)
April(4)
May(5)
June(6)
July(7)
August(8)
September(9)
October(10)
November(11)
December(12)
Average High
-2.3
-3.2
1.1
6.4
12.1
17.7
21.8
21.1
16.7
10.4
4.0
0.2
Using a graph, identify between which two months the rate of change is the greatest. Between which
two months is the rate of change the least?
The greatest rate of change is from October to November  m  6.4C/mnth  . The smallest rate of
change is from July to August  m  0.7C/mnth 
11. A 12-bottle case of motor oil costs $41.88. A mechanic needs to order 268 bottles of motor oil. If
he can only order by the case, how much money does he spend?
268
 22.3  23 cases
12
23  41.88  $963.24
12. (OMIT) A dinosaur model has a scale of 1:12. If the head of the dinosaur model is 8 cm in
length, how long is the head of the real dinosaur?
• What is the scale factor?
• What does this value mean?
• Will the value of the scale factor result in an enlargement or reduction? Explain.
• How did you determine the length of the head of the dinosaur?
13. A circle has been transformed so that its image radius is 14 cm. If the scale factor is 0.4, what is
the radius of the original circle?
dimension scale
k
dimension original
14
 0.4
x
0.4 x  14
0.4 x 14

0.4 0.4
x  35cm
14. (OMIT) ΔABC is similar to ΔSTU. If the sides of ΔABC measure 5.2, 3.8, and 6.4 respectively,
and the scale factor is 2:3, what is the perimeter of ΔSTU ?
15. A 4 in. by 6 in. picture has dimensions that have been tripled.
a) Find the new area using the relationship between the linear scale factor and the area scale factor.
Linear scale factor  k  3
Area scale factor  k 2  9
New area  24  9  216in 2
b) Find the new area using the linear scale factor only.
Linear scale factor  k  3
4  3  12; 6  3  18
New area  12 18  216in 2
16. (OMIT) Chad and Charlene painted a mural on the wall, measuring 12 ft by 8 ft using an
overhead projector. If the original sketch had an area of 216 in.2, what is the scale factor?
17. During an Art class, students are projecting the image of a can of Carnation milk on the wall.
The projector applies a scale factor of 250%. If the can has a diameter of 10 cm and a height of
12.5 cm, what are the dimensions of the image on the wall?
Linear scale factor  k  250% 
250
 2.5
100
New diameter  10  2.5  25cm
New height  12.5  2.5  31.25cm
18. Determine the scale factor that will produce the left image from the right image.
Scale Factor is 1:2 or
1
2
19. In the following blueprint, each square has a side length of 1/4in.
a) Ceramic tile costs $5 per square foot. How much would it cost to tile the bathroom?
3
 2

A   16    16   12  8  96ft 2
4
 4

96  5  $480
b) Carpet costs $18 per square yard. How much would it cost to carpet the bedroom and living
room?
5
 4

Abedroom   16    16   20  16  320ft 2  35.5yds 2
4
 4

4
 7

Aliving room   16    16   16  28  448ft 2  49.7yds 2
4
 4

35.5  49.7  18  85.3 18  $1536.00
c) Which has a higher unit cost, the tile or the carpet? Explain.
Tile
$5 / ft 2
Carpet
$18
 $2 / ft 2
2
9ft
Tile has the higher unit cost.
20. (OMIT) Mrs. Lewis intends to have the dining room redone with wood flooring that comes in 1
foot wide squares. The scale is 1 unit = 1ft. A 12 pack of squares sells for $38.40 and single
squares can be purchased for $3.70 each. Ask students to determine the cost, in dollars, for Mrs.
Lewis to buy just enough squares to cover her dining room floor?
21. Tony drew a scale diagram of his new skateboard to show a friend. He used a scale factor of 0.4.
The scaled diagram has dimensions 3.2 in. by 1.8 in. by 10.8 in. What are the dimensions of the
actual skateboard?
3.2
1.8
10.8
 8in;
 4.5in;
 27in
0.4
0.4
0.4
22. David claims that when you enlarge every side of a cube n times, its volume also increases n
times. Jane says that the volume of a cube increases 3n times, and Anne is convinced that the
volume increases n3 times. Who do you agree with and why?
If you enlarge every side of a cube n times, then the scale factor is n. Therefore k  n .
The results of this chapter indicate that
Since k  n , we know that
So Anne is correct.
volume scale
 k3 .
volume original
volume scale
 n3 .
volume original