Ten tickets to a cinema theater costs $66. What is the cost of 22 tickets to the same cinema theater?
It may be easier to find the cost c of one ticket (or unit rate) which is given by.
c = $66 / 10 tickets = 6.6 dollar / ticket
To find the cost C of 22 tickets, we just multiply the cost c of one ticket by 22
C = 22 tickets × c = 22 tickets × 6.6 dollars / ticket = $145.2
Cans of soda are packaged in boxes containing the same number of cans. There are 36 cans in 4 boxes.
a) How many cans are there in 7 boxes?
b) How many boxes are needed to package 99 cans of soda?
a) First find the number n of cans per box (unit rate).
n = 36 cans / 4 boxes = 9 cans / box
In 7 boxes we have N cans given by
N = 7 × n = 7 boxes × 9 cans / box = 63 cans
b) Let B be the number of boxes to package 99 cans. Use the rate to write an equation
9 cans / box = 99 cans / B
Cross multiply the fractions making the equation to obtain
9 cans × B = 99 cans × 1 box
Divide both sides by 9 cans and simplify
9 cans × B / 9 cans = 99 cans × 1 box / 9 cans
B = 11 boxes
Joe bought 4 kilograms of apples at the cost of $15. How much would he pay for 11 kilograms of the same apples in the same shop?
First find the cost c of one kilograms of apples (unit rate).
c = $15 / 4 kg = $3.75 / kg
Knowing the cost of 1 kg, the cost C of 11 kg is given by.
C = 11 kg × c = 11 kg × $3.75 / kg = $41.25
It takes a pump 10 minutes to move 55 gallons of water up a hill. Using the same pump under the same condition;
a) how much water is moved in 22 minutes?
b) how long does it take to move 165 gallons of water?
a) First find number of gallons n moved in one minute (unit rate).
A container with 324 liters of water, leaks 3 liters every 5 hours. How long does it take for the container to become empty?
Let T be the number of hours for 324 liters to be leaked. An equality of the rates gives
3 liters / 5 hours = 324 liters / T
Cross multiply the fractions in the above equation to obtain an equivalent equation.
3 liters × T = 5 hours × 324 liters
Divide both sides by 3 liters and simplify.
T = 5 hours × 324 liters / 3 liters = 540 hours
Twenty one cans of tomato paste of the same size have a weight of 7300 grams. What is the weight of 5 cans?
Let W be the weight of 5 cans. An equality of the rates gives
20 cans / 7300 grams = 5 cans / W
Cross multiply to obtain an equivalent equation.
20 cans × W = 5 cans × 7300 grams
Divide both sides by 20 cans and simplify.
W = 5 cans × 7300 grams / 20 cans = 1825 grams
An empty container is being filled with a water pump at the rate of 5 liters every 45 seconds. But the container also leaks water at the rate of one liter every 180 seconds. What is the quantity of water in the container after one hour?
In this problem we have two rates: one rate Rf at which water is being filled and the rate Rl at which water is being leaked. Find the two rates.
Rf = 5 liters / 45 seconds
Rl = 1 liter / 180 seconds
We also know that
1 hour = 3600 seconds
The quantity Q1 of water pumped after 1 hour is given by
Q1 = (5 liters / 45 seconds) × 3600 = 400 liters
The quantity Q2 of water lost through leakage after 1 hour is given by
Q2 = (1 liter / 180 seconds) × = 20 liters
The quantity Q of water in the container after 1 hour is given by