Example 1:
A motorcycle can travel 240 miles on 5 gallons of gasoline. Calculate the unit rate in miles per gallon.
Solution:
Simply divide 240 by 5 to solve this problem.
\(\frac{240~miles~\div ~5}{5~gallons~\div~5}=\frac{48~miles}{1~gallons}\)
The unit rate is 48 miles per gallon.
Hence, the motorcycle can cover 48 miles on a gallon of fuel.
Example 2:
Every 6 seconds, a jet plane travels 5 miles. Calculate the unit rate.
Solution:
The miles to seconds ratio is 5 :6. To get the unit rate in miles per second, divide by 6.
Hence, the unit rate is \(\frac{5}{6}\) miles per second.
Example 3:
A local store charges the following prices for jars of jelly. Find the best deal.
Solution:
The container with the lowest cost per unit is the best buy. That is, the jar of jelly that has the lowest unit rate in terms of cost per ounce is the best deal.
Divide the price of the jar by the number of ounces in it to get the cost per ounce for each jar. If necessary, round to the nearest thousandth.
Therefore, the 24-ounce jar has the lowest unit rate, and is hence the best buy because it has the lowest cost per ounce of $0.129.
Example 4:
Juice is available in two forms: cans with concentrated juice cans, and ready-to-serve cartons.
Which of the following options is the best buy?
12 oz can make 48 ounce of jouce for $1.69 60 oz cartoon for $2.59
Solution:
The best buy is the item that has the lowest cost per ounce of juice. That is, we need to buy the carton, either concentrated or ready to serve, that has the lowest unit rate in terms of cost per ounce.
To find that, divide the price by the ounces to determine the best buy.
For the concentrated cans, though the quantity in the can is only 12 ounces, using that we can make 48 ounces of juice. Hence, to find the unit rate, we take 48 ounces and not 12 ounces.
Concentrate \(\frac{$1.69}{48~ounces}=$0.0352\) per ounce
Carton \(\frac{$2.59}{60~ounces}=$0.0432\) per ounce
The concentrated cans are the better buy, even if you must mix it yourself, to take a sip!
