Using unit rates to make comparisons :
A rate is a comparison of two quantities that have different units.
To have better understanding on comparisons using unit rates, let us consider the example given below.
David has two job offers. One is paying $160 wages for 8 hours and other one is paying $95 wages for 5 hours. Can you help David to select the better job ?
In both the jobs, wages are given for different hours. To compare the two jobs, we have to convert the wages into unit rates.
That is, we have to find the wages for 1 hour.
In job 1 ,
Wages for 1 hour = 160/8 = $20 per hour
In job 2 ,
Wages for 1 hour = 95/5 = $19 per hour
When we compare the unit rates of both the jobs, Lily gets $1 more in the first job.
Hence, the first job is preferable.
Example 1 :
Lily 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 ?
To compare the costs, Lily must compare prices for equal amounts of juice.
That is, she 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 2 :
Michael drives 600 miles in 8 hours and Alex drives 380 miles in 5 hours. Who is driving faster ?
Distance covered by Michael in 1 hour is
= 600 / 8
= 75 miles per hour
Distance covered by Alex in 1 hour is
= 380 / 5
= 76 miles per hour
When we compare the above unit rates (Distance covered in 1 hour), Alex is driving faster than David.
After having gone through the stuff given above, we hope that the students would have understood "Using rates to make comparisons".
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