# COMPARING RATES WORKSHEET

Problem 1 :

Which is best,

10 pencils cost \$4

or

6 pencils cost \$2.70?

Problem 2 :

Which is best,

2 liters of milk at \$3.80

or

1.5 liters of milk at \$2.70?

Problem 3 :

Who is better in earning,

David earns \$57.60 in 8 hours

or

John earns \$90 in 12 hours?

Problem 4 :

Who is driving faster,

Alex covers 120 miles in 3 hours

or

Jose covers 84 miles in 2 hours?

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?

Problem 6 :

Which is best,

500 grams cheese cost \$ 3.25

or

1.5 kilograms cheese cost \$ 9.9

Problem 7 :

Who is driving faster,

Lenin  covers 6 miles in 2 minutes

or

Daniel covers 225 miles in 1.5 hours?

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?

Problem 9 :

Who is better,

Daniel answered 240 answers correctly out of 300 questions

or

Deborah answered 328 questions correctly out of 400 questions?

Problem 10 :

Which is best,

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

or

Plan B :  Income of \$280 on \$7000 investment 10 pencils cost \$4

or

6 pencils cost \$2.70

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.

2 liters of milk at \$3.80

or

1.5 liters of milk at \$2.70

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.

David earns \$57.60 in 8 hours

or

John earns \$90 in 12 hours

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 = \$90= 90/12= \$7.50

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

Hence, John is earning better.

Alex covers 120 miles in 3 hours

or

Jose covers 84 miles in 2 hours

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

 AlexDistance in 3 hrs : = 120 milesDistance 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.

Lily can prepare 10.4 gallons of juice in 4 days

or

Rosy can prepare 7.5 gallons of juice in 3 days

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.

500 grams cheese cost \$ 3.25

or

1.5 kilograms cheese cost \$ 9.9

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

 500 grams ----> \$3.251 kg. = 2 ⋅ 500 gramsPrice 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.

Lenin  covers 6 miles in 2 minutes

or

Daniel covers 225 miles in 1.5 hours

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 miles1 hour = 60 minutesDistance in 1 hr := 60 ⋅ 3 miles= 180 miles DanielDistance in 1.5 hrs := 225 milesDistance in 1 hr := 225/1.5 miles= 150 miles

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

Hence, Lenin is driving faster.

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

or

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

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.

Daniel answered 240 answers correctly out of 300 questions

or

Deborah answered 328 questions correctly out of 400 questions

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.

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

or

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

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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