Ratios
Are the ratios 4/5 and 9/10 proportional? Explain your reasoning.
No, they are not equivalent ratios. 4/5 = 8/10
There are 6 cups of pretzels in each box. How many cups of pretzels are there in five boxes?
30 cups
What two things must be true for a graph to show a proportional relationship?
Passes through the origin and is a straight line
Miranda has $30 to go to the local fair. She spends $5 on her entry ticket and the rest on games. Each game is $2.50, how many games can she play?
10 games
A proportional relationship is represented by the equation:
y=kx
When x=5, y=35, what is the value of the constant of proportionality, k?
7
If Andrew makes $22/hour, give an equation that models the situation where h represents hours and t represents total earnings
t = 22h
A car travels 157.5 miles in 3.5 hours. What speed is the car traveling?
45 mph
A map uses a scale of 1.5 cm : 5 km. If two cities are 3 cm apart, what is the real distance?
10 km
If Johnny can run 3 laps in 5 minutes, how many laps will be run in 8 minutes?
4.8 laps
A bicycle rental shop charges a proportional rate for renting a bicycle. It costs $18 to rent a bicycle for 3 hours.
Questions:
What is the constant of proportionality, k, representing the cost per hour?
6
y = 6x
Frank and Jack are having a pull-up contest. For every 6 pull-ups Frank does, Jack does 4. How many pull-ups will Frank do when Jack does 32?
48
For every 1/4 mile Pascal walks, Lucy runs 2/3 mile. How many miles does Pascal walk for every 1 mile Lucy runs?
3/8
A straight line passes through the points (0,0) and (1, 3/4). What is the equation that represents the relationship?
y = 3/4x
Josh uses a recipe for bubble solution that uses 1 cup of water and 1/4 cup of dish soap. If he uses 2 cups of dish soap, how much water should he use?
8 cups
Mrs. Love bought 5.25 pounds of sliced ham for $17. At that rate, what is the cost of 1 pound of sliced ham? Round to the nearest penny.
$3.24
In 30 minutes, 0.4 inches of rain falls. How many inches of rain will there be after 3 hours?
2.4 inches
What is the unit rate for the ratio 5/8 : 10/9
9/16
Jennifer buys clay for $0.50 per pound. What is the coordinate on the graph that would show the unit rate?
(1, 0.50)
Amy fills gift boxes at a rate of 9 boxes per hour. Carlos fills boxes at a rate of 7 boxes per hour. How many more boxes will Amy fill in 4 hours than Carlos?
8 boxes
Jovan charges $10 per hour to mow lawns in his neighborhood, plus $5 for showing up. Write an equation to relate how much Jovan is paid to mow a lawn to how many hours he works. Determine if the relation is proportional.
y = 10x + 5
Not proportional
If a marinade takes 1/4 cup of BBQ sauce and 1/2 cup of lemon juice, what is the ratio of lemon juice to marinade?
1/2 : 3/4
Yuki works 3 hours and makes $210. Give an equation that shows the constant of proportionality where x represents hours and y represents earnings.
y = 70x
A real car is 180 inches long. A toy car model of the same car is 6 inches long. What is the scale factor from the toy car to the real car?
30
A farm stand sells apples in 5-pound bags. Each bag costs $8.75. If cost is c, and p stands for pounds of apples - what is an equation that models the situation?
c = 1.75p
One batch of a recipe for bread requires 1/3 cups of cold water and 3/4 cup of oil. How much water will you need if you use 3 cups of oil?
12/9 = 1 1/3