**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 ?

**Answer :**

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

**Conclusion :**

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 ?

**Solution :**

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 ?

**Solution : **

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".

Apart from the stuff given above, if you want to know more about "Using unit rates to make comparisons", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**