Comparing rates worksheet are much useful to the students who would like to practice problems on comparing two measures for decision making.
Here we are going to look at markup and markdown worksheets - 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
Here they are .
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
Let us look at the next problem on "Comparing rates worksheet"
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
Let us look at the next problem on "Comparing rates worksheet"
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
Let us look at the next problem on "Comparing rates worksheet"
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
Let us look at the next problem on "Comparing rates worksheet"
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
Let us look at the next problem on "Comparing rates worksheet"
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 x 500 grams Price of 1 kg = 2 x 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
Let us look at the next problem on "Comparing rates worksheet"
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 1hr = 60x3 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
Let us look at the next problem on "Comparing rates worksheet"
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) x (7/1) Speed = 14 / 5 Speed = 2.8 miles per hour |
Declan Speed = (3/5) / (2/7) Speed = (3/5) x (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
Let us look at the next problem on "Comparing rates worksheet"
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] x 100 % Percent = 80 % |
Deborah Percent = [328 / 400] x 100 % Percent = 82 % |
From the above percentages, Deborah answered more questions correctly than Daniel per 100.
Hence, Deborah is better
Let us look at the next problem on "Comparing rates worksheet"
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] x 100% Percent of income = 5 % |
Plan B Percent = [280/7000] x 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
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