COMPARING RATES WORKSHEET
About "Comparing Rates Worksheet"
Comparing Rates Worksheet :
Worksheet given in this section is much useful to the students who would like to practice problems on comparing rates.
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Comparing Rates Worksheet - Problems
1. Which is best,
10 pencils cost $4
or
6 pencils cost $2.70 ?
2. Which is best,
2 liters of milk at $3.80
or
1.5 liters of milk at $2.70 ?
3. Who is better in earning,
David earns $57.60 in 8 hours
or
John earns $90 in 12 hours ?
4. Who is driving faster,
Alex covers 120 miles in 3 hours
or
Jose covers 84 miles in 2 hours ?
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 ?
6. Which is best,
500 grams cheese cost $ 3.25
or
1.5 kilograms cheese cost $ 9.9
7. Who is driving faster,
Lenin covers 6 miles in 2 minutes
or
Daniel covers 225 miles in 1.5 hours ?
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 ?
9. Who is better,
Daniel answered 240 answers correctly out of 300 questions
or
Deborah answered 328 questions correctly out of 400 questions ?
10. Which is best,
Plan A : Income of $250 on $5000 investment
or
Plan B : Income of $280 on $7000 investment
Let us look at step by step solution for each problem given on "Comparing rates worksheet".
Comparing Rates Worksheet - Solution
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 = $4 Cost of 1 pencil = 4/10 Cost of 1 pencil = $0.40 |
Cost of 6 pencils = $2.70 Cost of 1 pencil = 2.7/6 Cost 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 $3.80 Cost of 1 liter = 3.8/2 Cost of 1 liter = $1.90 |
2 liters of milk at $2.70 Cost of 1 liter = 2.7/1.5 Cost 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.
|
David Earning in 8 hrs = $57.60 Earning in 1 hr = 57.60/ 8 Earning in 1 hr = $7.20 |
John Earning in 12 hrs = $90 Earning in 1 hr = 90/12 Earning 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.
|
Alex Distance in 3 hrs = 120 miles Distance in 1 hr = 120 / 3 Distance in 1 hr = 40 miles |
Jose Distance in 2 hrs = 84 miles Distance 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.
|
Lily No.gallons in 2 days = 5.2 No.of gallons in 1 day = 5.2/2 No.of gallons in 1 day = 2.6 |
Rosy No. gallons in 3 days = 7.5 No. of gallons in 1 day = 7.5/3 No.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 -----> $3.25 1 kilogram = 2 ⋅ 500 grams Price of 1 kg = 2 ⋅ 3.25 Price of 1 kg = $6.5 |
1.5 kilograms -----> $9.9 Price of 1 kg = 9.9 / 1.5 Price 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.
|
Lenin Distance in 2 min = 6 miles Distance in 1 min = 3 miles 1 hour = 60 minutes Distance in 1 hr = 60 ⋅ 3 Distance in 1 hr = 180 miles |
Daniel Distance 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
|
Shanel Speed = (2/5) / (1/7) Speed = (2/5) ⋅ (7/1) Speed = 14 / 5 Speed = 2.8 miles per hour |
Declan Speed = (3/5) / (2/7) Speed = (3/5) ⋅ (7/2) Speed = 21 / 10 Speed = 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= [no. of correct answers / To tal no. of questions] x 100 %
|
Daniel Percent = [240/300] ⋅ 100 % Percent = 80 % |
Deborah Percent = [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.
After having gone through the stuff given on "Comparing rates worksheet", we hope that the students would have understood how to solve problems using unit rates.
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