USING UNIT RATES

We can use unit rates to simplify rates and ratios that appear complicated, such as those containing fractions in both the numerator and denominator.

To have better understanding on unit rates, let us look at the example given below.

Example :

Two tanks are getting leaked. After 15 minutes, Tank A has leaked 1/3 gallons of water. After 20 minutes, tank B has leaked 1/2 gallons of water. Which pool is leaking faster ?

To find which tank is leaking faster,  we have to find leak per hour for each pool.  

Compare the unit rates.

1.3 < 1.5

So, tank B is leaking faster. 

Solved Problems

Problem 1 :

A store had 2 packs of paper for $0.84. How much would it cost if you were to buy 3 packs ?

Solution :

The cost of one pack of paper is 

=  0.84 / 2

=  $0.42

The cost of 3 packs of paper is 

=  3 ⋅ 0.42

=  $1.26

Problem 2 :

A book store was selling 5 books for $38.40. Online the you could buy 6 books for $45.96. Which place has a lower unit price ?

Solution :

7.68 > 7.66

Comparing the unit prices in book store and online, online has lower unit price.  

Problem 3 :

At a comic book convention vendor 1 was selling a set of 4 comics for $30.88. Vendor 2 was selling a set of 3 comics for $22.98. Which vendor has the higher unit price ?

Solution :

7.72 > 7.66

Comparing the unit prices of vendor 1 and vendor 2, we have that vendor 1 has the higher unit price. 

Problem 4 :

In September a clothing store had a sale where you could get 3 scarves for $10.62. In October the price was changed to 4 scarves for $14.36. On which month did a scarf cost the most ?

Solution :

3.54 < 3.59

Comparing the unit prices of scarves in September and October, we have that unit price of scarf in October was higher.  

Problem 5 :

At a farming supply store 7 pounds of seeds cost $130.27. If a farmer needed 4 pounds of seeds, how much would it cost him ?

Solution :

The cost of 1 pound of seeds is 

=  130.27 / 7

=  $18.61

The cost of 4 pounds of seeds is 

=  4 ⋅ 18.61

=  $74.44

Problem 6 :

At the baseball stadium the price for popcorn is $7.64 for 4 bags. If you wanted to buy 5 bags of popcorn, how much would it cost ?

Solution :

The cost of 1 bag of popcorn is 

=  7.64 / 4

=  $1.91

The cost of 5 bags of popcorn is

=  5 ⋅ 1.91

=  $9.55

Problem 7 :

A shoe store was having a back to school sale where you could buy 6 pairs of shoes for $124.68. If a large family decided to buy 2 pairs of shoes, how much would it cost them ?

Solution :

The cost of 1 pair of shoes is 

=  124.68 / 6

=  $20.78

The cost of 2 pairs of shoes is 

=  2 ⋅ 20.78

=  $41.56

Problem 8 :

At the toy store you could get 3 board games for $17.88. Online the price for 6 board games is $36.30. Which place has the highest price for a board game ?

Solution :

5.96 < 6.05

Comparing the unit prices in toy store and online, online has the highest price.  

Problem 9 :

An ice company charged $6.40 for 5 bags of ice. If a convenience store bought 7 bags of ice, how much would it have cost them ?

Solution :

The cost of 1 bag of ice is 

=  6.40 / 5

=  $1.28

The cost of 7 bags of ice is

=  7 ⋅ 1.28

=  $8.96

Problem 10 :

On Monday the price for bottled water was 3 bottles for $4.17. On Saturday the price was 4 bottles for $5.60. Which day had the higher unit price ?

Solution :

1.39 < 1.40

Comparing the unit prices on Monday and Saturday, we have that the unit price on Saturday is higher.

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