Comparing rates :
"Comparing rates" is nothing but comparing 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 Cost of 1 doll = $ 15 |
6 dolls cost $102 Cost of 1 doll = 102 / 6 Cost of 1 doll = $ 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.
To have better understanding on comparing unit rates, let us look some practice 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 = $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"
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"
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"
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"
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"
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"
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"
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"
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"
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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