USING RATES TO COMPARE PRICES

A rate is a comparison of two quantities that have different units.

Let us look at some examples to understand how rates can be used to compare prices.

Example 1 :

Lily has two job offers. One is paying $160 for 8 hours and other one is paying $95 for 5 hours. Can you help Lily to choose the better job?

Solution :

In both the jobs, salary is given for different hours. To compare the two jobs, we have to convert the salaries into unit rates.

That is, we have to find the salary for 1 hour.

In job 1,

salary for 1 hour = 160/8 = $20 per hour  

In job 2 ,

salary for 1 hour = 95/5 = $19 per hour

Conclusion :

When we compare the unit rates of both the jobs, Lily gets $1 more in the first job.

So, the first job is preferable.

Example 2 :

Michael is at the grocery store comparing two brands of juice. Brand A costs $3.84 for a 16-ounce bottle. Brand B costs $4.50 for a 25-ounce bottle. Which brand is the better buy?

Solution :

To compare the costs, Michael must compare prices for equal amounts of juice.

That is, he has to compare prices of one ounce of each juice.

We can get the price of 1 ounce of each juice as given below. 

From the above tables,

brand A costs = $0.24 per ounce

brand B costs = $0.18 per ounce

When we compare the unit prices of the two brands given above, it is better to buy brand B.

Example 3 :

David covers 600 miles in 8 hours and John covers 380 miles in 5 hours. Who is driving faster?

Solution :

Distance covered by David in 1 hour is

= 600/8 

= 75 miles per hour

Distance covered by John in 1 hour is

= 380/5 

= 76 miles per hour

When we compare the above unit rates (Distance covered in 1 hour), John is driving faster than David.

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