# COMPARING RATES

In this section, you will learn, how to compare the given two measures by converting them into unit rates.

Example :

Compare "8 dolls cost \$120" and "6 dolls cost \$102".

To compare the given measures, convert than in to unit rates.

 8 dolls cost \$120Cost of 1 doll  =  120 / 8Cost of 1 doll  =  \$ 15 6 dolls cost \$102Cost of 1 doll  =  102 / 6Cost of 1 doll  =  \$ 17

" 8 dolls cost \$120" is less than "6 dolls cost \$102"

Because, unit rate in "8 dolls cost \$120" is \$15. But the unit rate in  "6 dolls cost \$102" is \$17.

## Solved Problems

Problem 1 :

Which is best,

10 pencils cost \$4

or

6 pencils cost \$2.70 ?

Solution :

To compare the given measures, convert them in to unit rates.

 Cost of 10 pencils  =  \$4Cost of 1 pencil  =  4/10Cost of 1 pencil  =  \$0.40 Cost of 6 pencils  =  \$2.70Cost of 1 pencil  =  2.7/6Cost of 1 pencil  =  \$0.45

We get the lowest price per pencil \$0.40 in "10 pencils cost \$4"

Hence, "10 pencils cost \$4" is the best deal.

Problem 2 :

Which is best,

2 liters of milk at \$3.80

or

1.5 liters of milk at \$2.70 ?

Solution :

To compare the given measures, convert them in to unit rates.

 2 liters of milk at \$3.80Cost of 1 liter  =  3.8/2Cost of 1 liter  =  \$1.90 2 liters of milk at \$2.70Cost of 1 liter  =  2.7/1.5Cost of 1 liter  =  \$1.8

From the above unit rates, we get the lower price per liter of milk \$1.8 in "2 liters cost \$2.70"

Hence, "2 liters cost \$2.70" is the best deal.

Problem 3 :

Who is better in earning,

David earns \$57.60 in 8 hours

or

John earns \$90 in 12 hours ?

Solution :

To compare the given measures, convert them in to unit rates.

 DavidEarning in 8 hrs  =  \$57.60Earning in 1 hr  =  57.60/8Earning in 1 hr  =  \$7.20 JohnEarning in 12 hrs = \$90Earning in 1 hr  =  90/12Earning in 1 hr  =  \$7.50

From the above unit rates, John earns more than David per hour.

Hence, John is earning better.

Problem 4 :

Who is driving faster,

Alex covers 120 miles in 3 hours

or

Jose covers 84 miles in 2 hours ?

Solution :

To compare the given measures, convert them in to unit rates.

 AlexDistance in 3 hrs  =  120 miles Distance in 1 hr  =  120/3 Distance in 1 hr  =  40 miles JoseDistance in 2 hrs  =  84 milesDistance in 1 hr  =  84/2 Distance in 1 hr  =  42 miles

From the above unit rates, Jose covers more miles than David per hour.

Hence, Jose is driving faster.

Problem 5 :

Who is better,

Lily can prepare 10.4 gallons of juice in 4 days

or

Rosy can prepare 7.5 gallons of juice in 3 days ?

Solution :

To compare the given measures, convert them in to unit rates.

 LilyNo.gallons in 2 days  =  5.2No.of gallons in 1 day = 5.2/2No.of gallons in 1 day = 2.6 RosyNo. gallons in 3 days  =  7.5No. of gallons in 1 day = 7.5/3No.of gallons in 1 day = 2.5

From the above unit rates, Lily prepares more gallons than day.

Hence, Lily is better.

Problem 6 :

Which is best,

500 grams cheese cost \$ 3.25

or

1.5 kilograms cheese cost \$ 9.9

Solution :

To compare the given measures, convert them in to unit rates in price per kilogram.

 500 grams -----> \$3.251 kilogram  =  2 ⋅ 500 grams Price of 1 kg  =  2 ⋅ 3.25Price of 1 kg  =  \$6.5 1.5 kilograms -----> \$9.9Price of 1 kg  =  9.9 / 1.5Price of 1 kg  =  \$6.6

From the above unit rates, we get the lower price per kilogram \$6.5 in "500 grams cheese cost \$ 3.25"

Hence, "500 grams cheese cost \$ 3.25" is the best deal.

Problem 7 :

Who is driving faster,

Lenin  covers 6 miles in 2 minutes

or

Daniel covers 225 miles in 1.5 hours ?

Solution :

To compare the given measures, convert them in to unit rates in distance per hour.

 LeninDistance in 2 min  =  6 miles Distance in 1 min  =  3 miles 1 hour  =  60 minutesDistance in 1 hr  =  60 ⋅ 3Distance in 1 hr  =  180 miles DanielDistance in 1.5 hrs = 225 miles Distance in 1 hr  =  225 / 1.5 Distance in 1 hr  =  150 miles

From the above unit rates, Lenin covers more miles than Daniel per hour.

Hence, Lenin is driving faster.

Problem 8 :

Who is better in walking,

Shanel walks 2/ 5 of a mile every 1/7 hour.

or

Declan walks 3/5 of a mile every 2/7 hour ?

Solution :

To compare the given measures, convert them in to unit rates in miles per hour (speed).

Speed  =  Distance / Time

 ShanelSpeed  =  (2/5)  /  (1/7)Speed  =  (2/5)  ⋅  (7/1)Speed  =  14 / 5Speed  =  2.8 miles per hour DeclanSpeed  =  (3/5)  /  (2/7)Speed  =  (3/5)  ⋅  (7/2)Speed  =  21 / 10Speed  =  2.1 miles per hour

From the above unit rates, Shanel walk more miles than Declan per hour.

Hence, Shanel is better in walking.

Problem 9 :

Who is better,

or

Deborah answered 328 questions correctly out of 400 questions ?

Solution :

To compare the given measures, convert them in to percentages .

Percent is

= [no. of correct answers/ Total no. of questions] x 100 %

 DanielPercent = [240/300] ⋅ 100 %Percent = 80 % DeborahPercent = [328/400] ⋅ 100 %Percent = 82 %

From the above percentages, Deborah answered more questions correctly than Daniel per 100.

Hence, Deborah is better.

Problem 10 :

Which is best,

Plan A :  Income of \$250 on \$5000 investment

or

Plan B :  Income of \$280 on \$7000 investment

Solution :

To compare the given measures, convert them in to percentages of income .

Percent of income  =  [Income / Investment] x 100 %

 Plan A Percent = [250/5000] ⋅ 100%Percent of income  =  5 % Plan B Percent = [280/7000] ⋅ 100%Percent of income  =  4 %

From the above percentages, plan A gives more income than plan B per \$100 investment.

Hence, plan A is better. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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