# 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 = 120/8= \$15 6 dolls cost \$102Cost of 1 doll = 102/6= \$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 = 4/10= \$0.40 Cost of 6 pencils = \$2.70Cost of 1 pencil = 2.7/6= \$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 = 3.8/2= \$1.90 2 liters of milk at \$2.70Cost of 1 liter = 2.7/1.5= \$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 = 57.60/8= \$7.20 JohnEarning in 12 hrs = \$90Earning in 1 hr = 90/12= \$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 = 40 miles JoseDistance in 2 hrs = 84 milesDistance in 1 hr = 84/2 = 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 := 5.2/2= 2.6 RosyNo. gallons in 3 days : = 7.5No. of gallons in 1 day := 7.5/3= 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(3.25)= \$6.5 1.5 kilograms ----> \$9.9Price of 1 kg : = 9.9/1.5= \$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 milesDistance in 1 min : = 3 miles 1 hour = 60 minutesDistance in 1 hr : = 60(3)= 180 miles DanielDistance in 1.5 hours : = 225 miles Distance in 1 hour := 225/1.5 = 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)= (2/5) ⋅ (7/1)= 14/5= 2.8 miles per hour DeclanSpeed = (3/5)/(2/7)= (3/5) ⋅ (7/2)= 21/10= 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,

Daniel answered 240 answers correctly out of 300 questions

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%= 80% DeborahPercent : = [328/400] ⋅ 100%= 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 of income := [250/5000] ⋅ 100% = 5% Plan B  Percent of income := [280/7000] ⋅ 100%= 4%

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

Hence, plan A is better.

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