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 $120 Cost of 1 doll = 120/8 = $15 |
6 dolls cost $102 Cost 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.
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 = $0.40 |
Cost of 6 pencils = $2.70 Cost 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 $3.80 Cost of 1 liter = 3.8/2 = $1.90 |
2 liters of milk at $2.70 Cost 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.
David Earning in 8 hrs = $57.60 Earning in 1 hr = 57.60/8 = $7.20 |
John Earning in 12 hrs = $90 Earning 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.
Alex Distance in 3 hrs = 120 miles Distance in 1 hr = 120/3 = 40 miles |
Jose Distance in 2 hrs = 84 miles Distance 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.
Lily No. gallons in 2 days : = 5.2 No. of gallons in 1 day : = 5.2/2 = 2.6 |
Rosy No. gallons in 3 days : = 7.5 No. 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 ----> $3.25 1 kilogram = 2(500) grams Price of 1 kg : = 2(3.25) = $6.5 |
1.5 kilograms ----> $9.9 Price 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.
Lenin Distance in 2 min : = 6 miles Distance in 1 min : = 3 miles 1 hour = 60 minutes Distance in 1 hr : = 60(3) = 180 miles |
Daniel Distance 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
Shanel Speed = (2/5)/(1/7) = (2/5) ⋅ (7/1) = 14/5 = 2.8 miles per hour |
Declan Speed = (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%
Daniel Percent : = [240/300] ⋅ 100% = 80% |
Deborah Percent : = [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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