Solved Examples and Worksheet for Unit Rates

Q1Jerald and his brother George agreed to divide their flock of sheep equally. But, Jerald takes 50 sheep and George takes 60, for which George pays $150 to Jerald. What is the cost of each sheep?
A. $15
B. $42
C. $30
D. $35
E. $33

Solutions
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Step: 1
Jerald and George agree to divide their flock of sheep equally but Jerald and George took 50 and 60 sheep respectively.
Step: 2
So George took 5 extra sheep, for which, he paid $150 to Jerald.
Step: 3
Therefore, the cost of each sheep = 1505 = $30.
Correct Answer is :   $30
Q2Ashley bought 3 pounds of apples for $0.72. Find the cost of one pound of apple.
A. $0.24
B. $3.72
C. $2.28
D. $2.16

Solutions
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Step: 1
The cost of each pound of apples that Ashley bought = Total cost of 3 pounds of applesNumber of pounds of apples.
Step: 2
= 0.723
  [Substitute the values.]
Step: 3
= $0.24
  [Divide.]
Step: 4
The cost of one pound of apples is $0.24.
Correct Answer is :   $0.24
Q3Jerald wrote a 96 page report in 6 hours. What is his unit rate of writing?
A. 16 pages/hour
B. 90 pages/hour
C. 102 pages/hour
D. 576 pages/hour

Solutions
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Step: 1
Unit rate = total pages writtentime taken in hours = 966
Step: 2
= 96÷66÷6= 161
  [Divide numerator and denominator by 6.]
Step: 3
Jerald's unit rate of writing is 16 pages per hour.
Correct Answer is :   16 pages/hour
Q4Kelsey earned $228 for 38 hours of work. Find the unit rate.
A. $6 per hour
B. $8 per hour
C. $5 per hour
D. $7 per hour

Solutions
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Step: 1
Unit rate = amount earnednumber of hours.
= 22838 = 6
  
Step: 2
The unit rate is $6 per hour.
Correct Answer is :   $6 per hour
Q5A 7-ounce tomato has about 35 calories. What is the unit rate?
A. 7 calories/ounce
B. 5 calories/ounce
C. 6 calories/ounce
D. 4 calories/ounce

Solutions
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Step: 1
Unit rate = caloriesounce = 357 = 5 .
Step: 2
The unit rate of tomato is 5 calories/ounce.
Correct Answer is :   5 calories/ounce
Q6Charlie received 117 telephone calls in 13 hours. Find the unit rate.

A. 9 calls/hour
B. 10 calls/hour
C. 11 calls/hour
D. 8 calls/hour

Solutions
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Step: 1
Unit rate = telephone callshours = 11713= 9.
Step: 2
Unit rate is 9 calls/hour.
Correct Answer is :   9 calls/hour
Q7The hair in a typical man's beard grows about 3.9 mm per week. What is the unit rate of growth in mm per day?
A. 0.59 mm per day
B. 0.53 mm per day
C. 0.56 mm per day
D. 0.48 mm per day

Solutions
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Step: 1
Unit rate = size of the beard growsnumber of days = 3.97
Step: 2
= 3.9÷77÷7 = 0.561
  [Divide both numerator and denominator by denominator.]
Step: 3
The growth rate of the man's beard is 0.56 mm/day.
Correct Answer is :   0.56 mm per day
Q8Which would be a better buy, 8 pencils for $4.40 or 13 pencils for $6.5?
A. 8 pencils for $4.40
B. 13 pencils for $6.5
C. cannot be determined
D. none of these

Solutions
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Step: 1
The unit price of 8 pencils
= costnumber = 4.408 = $0.55 per pencil
  [Express as a ratio and simplify.]
Step: 2
The unit price of 13 pencils.
= costnumber = 6.513 = $0.5 per pencil
  [Express as a ratio and simplify.]
Step: 3
The unit rate of second one is less than the first, so the second one is a better buy.
Correct Answer is :   13 pencils for $6.5
Q9Which would be a better buy, 7 highlighters for $2.45 or 10 highlighters for $3?

A. 7 highlighters for $2.45
B. 10 highlighters for $3
C. cannot be determined
D. none of these

Solutions
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Step: 1
Unit rate of first kind of highlighters = costnumber = 2.457 = $0.35 per highlighter
  [Express as a ratio and simplify.]
Step: 2
Unit rate of second kind of highlighters = costnumber = 310 = $0.30 per highlighter
  [Express as a ratio and simplify.]
Step: 3
The unit rate of second one is less than the first, so the second one is a better buy.
Correct Answer is :   10 highlighters for $3
Q10The cost of 6 lb of sugar of Quality-A is $24 and cost of 9 lb of sugar of Quality-B is $46.80. Which is a better buy?

A. Sugar of Quality-B
B. Cannot be determined
C. Sugar of Quality-A
D. none of these

Solutions
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Step: 1
The unit rate of sugar of Quality-A = $246
Step: 2
= 24÷66÷6 = $41
  [Divide both the numerator and the denominator by the denominator.]
Step: 3
The unit rate of sugar of Quality-B = $46.809
Step: 4
= 46.80÷99÷9 = $5.201
  [Divide both the numerator and the denominator by the denominator.]
Step: 5
As the unit rate of Quality-A sugar is less than the unit rate of Quality-B sugar, it is better to buy sugar of Quality-A.
Correct Answer is :   Sugar of Quality-A
Q11A 9 fl.oz bottle of orange juice costs $70 and 14 fl.oz bottle of orange juice costs $140. Which is a better buy?
A. 9 fl.oz bottle
B. 14 fl.oz bottle
C. Cannot say
D. None of these

Solutions
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Step: 1
Unit rate 1 = Juice costquantity of bottle = 709 = $0.77
  [Write the unit rate for 9 fl.oz bottle.]
Step: 2
Unit rate 2 = Juice costquantity of bottle = 14014 = $1
  [Write the unit rate for 14 fl.oz bottle.]
Step: 3
The unit rate of the first one is less than the second one. So, The first one is a better buy.
Correct Answer is :   9 fl.oz bottle
Q12A ribbon of 4 yd length costs $20. The same ribbon of 7 yd length costs $28. Which ribbon is a better buy?

A. 7 yd
B. 4 yd
C. Either 4 yd or 7 yd
D. cannot be determined

Solutions
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Step: 1
The unit cost of the 4 yd length of ribbon = pricelength
= $204yd = $5yd
  
Step: 2
The unit cost of the 7 yd length of ribbon = pricelength
= $287yd= $4yd.
  
Step: 3
4 < 5
  [Compare the two prices.]
Step: 4
The unit cost of 7 yd length ribbon is less than the unit cost of 4 yd length ribbon.
Step: 5
So, it is better to buy 7 yd length of the ribbon.
Correct Answer is :   7 yd
Q13Andy went to a movie with his family. He spent $54 for 6 tickets. What is the cost of each ticket?

A. $15
B. $324
C. $9

Solutions
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Step: 1
Money spent = $54
Step: 2
Number of tickets = 6
Step: 3
Cost of each ticket = Total money spent on ticketsNumber of tickets
Step: 4
= $546 = $9
  [Substitute the values and divide.]
Step: 5
So, the cost of each ticket is $9.
Correct Answer is :   $9
Q14At a grocery store, 4 gallons of milk costs $16. Find the cost of a gallon of milk.

A. $6 per gallon
B. $5 per gallon
C. $4 per gallon
D. $3 per gallon

Solutions
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Step: 1
costquantity = 164
  [Express the comparison as a ratio.]
Step: 2
= 16 ÷ 44 ÷ 4
  [Divide both the numerator and the denominator by the denominator.]
Step: 3
= 41
  [Simplify.]
Step: 4
The unit rate of milk is $4 per gallon.
Correct Answer is :   $4 per gallon
Q15A motorcycle has covered 324 miles in 6 hours. Find the unit rate in mi/hr.

A. 54 mi/hr
B. 48 mi/hr
C. 57 mi/hr
D. 60 mi/hr

Solutions
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Step: 1
mileshours = 3246
  [Write the comparison as a ratio.]
Step: 2
= 324 ÷ 66 ÷ 6
  [Divide both the numerator and the denominator by the denominator.]
Step: 3
= 541
  [Simplify.]
Step: 4
The unit rate is 54 mi/ hr.
Correct Answer is :   54 mi/hr

HighSchool Math