Unit Rate & Best Buy
Tables & Constants
Graphs & Meaning
Equations & Proportions
Scale & Mixed Review
Final Jeopardy
100
A pet store sells 8 chew toys for $22.40. What is the cost per toy?
Answer: $2.80 per toy
cost per toy
22.40/8 = 2.80
100
Find the constant of proportionality: items per box.
Boxes | Items
5 | 110
8 | 176
12 | 264
Answer: 22 items per box
item per box
110/5 = 22
176/8 = 22
264/12 = 22
100
Does the graph represent a proportional relationship? Explain.
Answer: Yes. It is a straight line through the origin.
100
The total cost y of x pounds of peaches is represented by y = 3.75x. What does 3.75 represent?
Answer:
The cost of 1 pound of peaches: $3.75 per pound.
y/x = cost/pounds= cost per pound
100
A model uses the scale 1 inch = 14 feet. A wall on the model is 4.5 inches long. What is the actual length?
Answer: 63 feet
100
A school orders 7 1/2 cases of water for $123.75. The cost is proportional to the number of cases.
A) Find the cost per case.
B) Write an equation for total cost c in terms of cases n.
C) Use your equation to find the cost of 12 2/3 cases of water.
Answers:
A $123.75 /(7 1/2) = $16.50 per case
B. c=16.50n
C. c = 16.50 n
c = 16.50 x 12 2/3
c = $209
200
A landscaper spreads 3 3/4 bags of seed over 600 square feet. At the same rate, how many square feet can be covered by 1 bag?
Answer: 160 feet2 per bag
feet per bag
600 / (3 3/4 ) = 160
200
Is the relationship proportional? Explain.
x | y
6 | 9
10 | 15
14 | 21
18 | 27
Answer: The table is proportional because there is a constant of proportionality of 1.5
y/x
9/6=1.5
15/10=1.5
21/14=1.5
27/18=1.5
200
Which point on this graph represents the unit rate?
Answer: (1, 18)
In a proportional graph, the unit rate is always the y-coordinate when the x-coordinate is 1: (1,__)
200
Write an equation that represents the table?
x | y
8 | 2
14 | 3.5
20 | 5
26 | 6.5
Answer:
y =1/4 x
y/x =2/8=1/4
y/x=3.5/14=1/4
y/x=4/20=1/4
y/x=6.5/26=1/4
200
A map uses the scale 1 centimeter = 45 miles. Two cities are 292.5 miles apart. How far apart are they on the map?
Answer: 6.5 centimeters
300
Which is the better buy?
A: 4 notebooks for $7.40
B: 6 notebooks for $10.50
C: 9 notebooks for $15.93
Answer B.
Better buy means the cheapest cost.
cost per notebook
A:
7.40/4 =1.85
B:
10.50/6 = 1.75
C:
15.93/9 = 1.77
300
Is the relationship proportional? Explain.
x | y
4 | 7
8 | 14
12 | 21
16 | 29
Answer: The table is not proportional because there is not a constant ratio.
y/x
7/4=1.75
14/8=1.75
21/12=1.75
29/16=1.8125
300
The point (6, 90) is on the graph. Explain what this point means in context if x is number of people and y is total admission cost.
Answer: Admission for 6 people costs $90.
300
A theater charges the same price for every ticket.
Six tickets cost $81.
Write an equation for total cost c in terms of number of tickets t.
Answer: c = 13.5t
cost per ticket
k=81/6=13.50
300
On a drawing, 3/4 inch represents 4 1/2 feet. How many feet does 2 1/4 inches represent?
Answer: 13 1/2
400
A machine uses 5 1/4 gallons of fuel in 2 1/3 hours. At a constant rate, how many gallons does it use per hour?
Answer:
2 1/4
gallons per hour
gallon per hour
(5 1/4)/(2 1/3)= 2 1/4
400
The table is proportional. Find the missing distance.
Gallons | Miles
2 | 42
3.5 | ?
6 | 126
8 | 168
Answer: 73.5 miles
miles per gallon
42/2 =21
3.5 *21 = 73.5
400
The graph shows earnings versus hours. What is the hourly wage?
Answer: $14.50 per hour
Pick a point that you can read on graph without estimating- anything but (0,0)
Divide y/x
(4,58)= y/x=58/4=14.5
(10,145)=y/x=145/10=14.5
400
A recipe uses 2 1/4 cups of broth for 3/4 cup of rice. Write a proportion that could be used to find b, the cups of broth needed for 2 1/2 cups of rice.
Answer:
or any other proportion with the same cross products.
400
A farmer pays $14.40 for 6 pounds of tomatoes. At the same rate, what would 17.5 pounds cost? Show a proportional method.
$42.00
500
A reader finishes 6 2/3 pages in 16 minutes. At the same rate, how many pages per hour does the reader finish?
Answer: 25 pages per hour
pages per hour
16 minutes =
16/ 60 = 4/15 hr
(6 2/3)/(4/15) = 25
500
Which statement best describes the relationship below?
m | k
12 | 19.308
25 | 40.225
38 | 61.142
A. Proportional because k/m is constant
B. Proportional because k − m is constant
C. Not proportional because k/m is constant
D. Not proportional because k − m is constant
Answer: A: The ratio k/m is constant (1.609).
k divided by m
19.308/12=1.609
40.225/25=1.609
61.142/38=1.609
500
Tank A begins with 500 gallons and then fills at a constant rate. Tank B begins empty and fills at a constant rate.
For each tank, decide whether amount of water is proportional to time. Explain. If proportional, give the unit rate.
Answer:
Tank A: Not proportional because the straight line does not pass through the origin, (0,0).
Tank B: Proportional because it is straight line that passes through the origin. The unit rate is 300 gallons per minute.
(2,600)=y/x=600/2=300
500
A robot travels 7 feet in 12 seconds at a constant speed.
Part A: Write an equation for distance d in terms of time t.
Part B: Use it to find the distance traveled in 30 seconds.
Answer:
d=7/12t; d=17.5
d=7/12t
d=7/12*30
d=17.5
500
A trail map uses 1 1/2 inches to represent 6 miles. Two locations are 8 3/4 inches apart on the map.
Write and solve a proportion to find the actual distance.
35 miles