Application of Proportions involving Unit Prices-Gr 7-Solved Examples

Solved Examples and Worksheet for Application of Proportions involving Unit Prices

Q1The cost of 9 pizzas is $19. Find the cost of 27 pizzas.

A. $57
B. $69
C. $114
D. $67

Solutions

Step: 1

Let n be the cost of 27 pizzas.

Step: 2

919 = 27n

[Write a possible proportion.]

Step: 3

9 × n = 19 × 27

[Write the cross products.]

Step: 4

9 × n = 513

[Multiply.]

Step: 5

9n9 = 5139

[Divide each side by 9.]

Step: 6

n = 57

Step: 7

The cost of 27 pizzas is $57.

Correct Answer is : $57

Q2At a fair 4 rides on a horse cost $10. Find the number of rides Andrew enjoyed, if he pays a total of $20.

A. 9
B. 7
C. 8
D. 10

Solutions

Step: 1

Let n be the number of horse rides Andrew enjoyed.

Step: 2

410 = n20

[Write a proportion in terms of ridesamount.]

Step: 3

4 × 20 = 10 × n

[Write the cross products.]

Step: 4

80 = 10n

[Multiply.]

Step: 5

8010 = 10n10

[Divide both sides by 10.]

Step: 6

8 = n

Step: 7

Number of rides Andrew enjoyed is 8.

Correct Answer is : 8

Q3A museum charges $5.50 per person as an entry ticket. If a family paid $44 for the tickets, then find the number of people in the family.
A. 15
B. 8
C. 10
D. 6

Solutions

Step: 1

Let n be the total number of people in the family.

Step: 2

numberentry fee, n44 = 15.50

[Write a possible proportion.]

Step: 3

5.50 × n = 44 × 1

[Write the cross products.]

Step: 4

5.50 n = 44

[Multiply.]

Step: 5

5.50n5.50 = 445.50

[Divide both sides by 5.50.]

Step: 6

n = 8

Step: 7

The total number of members in the family = 8.

Correct Answer is : 8

Q4Brian bought 5 lb of candy for $25. Find the unit rate.
A. $7/lb
B. $5/lb
C. $4/lb
D. $6/lb

Solutions

Step: 1

Rate = costweight

Step: 2

= $255lb

[Substitute the values.]

Step: 3

= $5/lb

[Simplify.]

Step: 4

The unit rate is $5/lb.

Correct Answer is : $5/lb

Q5William bought 5 cups of milk for $4. Find the unit rate.

A. $2.80/cup
B. $0.80/cup
C. $4.80/cup
D. None of the above

Solutions

Step: 1

Rate = $45cups = $0.80/cup

Step: 2

The unit rate is $0.80/cup.

Correct Answer is : $0.80/cup

Q6Josh bought 3 pizzas for $2.50. How much would he pay for 6 pizzas? (Use proportions to find the amount.)

A. $4
B. $6
C. $15
D. $5

Solutions

Step: 1

Let $x be the required amount.

Step: 2

32.50 = 6x

[Write a proportion.]

Step: 3

3 × x = 6 × 2.5

[Cross multiply.]

Step: 4

3x = 15

[Multiply.]

Step: 5

x = 5

[Simplify.]

Step: 6

So, Josh has to pay $5 in order to buy 6 pizzas.

Correct Answer is : $5

Q7Find the cost of 30 books, if 6 books cost $4. Assume each book costs the same.
A. $20
B. $23
C. $24
D. $22

Solutions

Step: 1

Let n be the cost of 30 books.

Step: 2

46 = n30

[Write a possible proportion.]

Step: 3

6 × n = 30 × 4

[Write the cross products.]

Step: 4

6n = 120

[Multiply.]

Step: 5

6n6 = 1206

[Divide both sides by 6.]

Step: 6

n = 20

[Simplify.]

Step: 7

The cost of 30 books is $20.

Correct Answer is : $20

Q8Jim bought 4 dozen blackberries for $16. How many blackberries would Jim get for $24?

A. 6 dozens
B. 9 dozens
C. 8 dozens
D. 7 dozens

Solutions

Step: 1

Let n be the number of dozens Jim bought.

Step: 2

416 = n24

[Write a proportion.]

Step: 3

4 × 24 = 16 × n

[Write the cross products.]

Step: 4

96 = 16n

[Multiply.]

Step: 5

9616 = 16n16

[Divide both sides by 16.]

Step: 6

6 = n

Step: 7

Jim would get 6 dozens for $24.

Correct Answer is : 6 dozens

Q9The cost of 9 pastries is $19. Find the cost of 27 pastries.

A. $57
B. $67
C. $114
D. $69

Solutions

Step: 1

Let n be the cost of 27 pastries.

Step: 2

919 = 27n

[Write a possible proportion.]

Step: 3

9 × n = 19 × 27

[Write the cross products.]

Step: 4

9 × n = 513

[Multiply.]

Step: 5

9n9 = 5139

[Divide each side by 9.]

Step: 6

n = 57

Step: 7

The cost of 27 pastries is $57.

Correct Answer is : $57

Q10The cost of 3 pens is $27. Which proportion could be solved to find x, the cost of 9 pens?

A. 327 = x9
B. 927 = 3x
C. 327 = 9x
D. 273 = 9x

Solutions

Step: 1

Cost of 3 pens = $27

Step: 2

Let x be the cost of 9 pens.

Step: 3

327 = 9x

[Write the proportion.]

Step: 4

So, cost of 9 pens can be found using the proportion 327 = 9x

Correct Answer is : 327 = 9x

Q11George earns $8 per hour. How many dollars will he earn, if he works for 6 hours?
A. $42
B. $48
C. $14
D. $40

Solutions

Step: 1

16= 8n

[Write a possible proportion.]

Step: 2

n × 1 = 6 × 8

[Write the cross products.]

Step: 3

n = 48

Step: 4

George will earn $48, if he works for 6 hours.

Correct Answer is : $48

Q12Select the best deal.
A. 5 fl oz bottle for $25
B. 3 fl oz bottle for $18
C. 2 fl oz bottle for $12
D. 10 fl oz bottle for $65

Solutions

Step: 1

If the unit price of an item is the lowest compared to others, then that item is said to be the best deal.

Step: 2

Unit price of one fl ounce of bottle = costnumber

Step: 3

In case of '10 fl oz bottle for $65', the unit cost = 6510 = $6.5

[Express as a ratio and simplify.]

Step: 4

In case of ' 2 fl oz bottle for $12', the unit cost = 122 = $6

[Express as a ratio and simplify.]

Step: 5

In case of '5 fl oz bottle for $25', the unit cost = 255 = $5

[Express as a ratio and simplify.]

Step: 6

In case of ' 3 fl oz bottle for $18 ', the unit cost = 183 = $6

[Express as a ratio and simplify.]

Step: 7

Therefore, '5 fl oz bottle for $25' is the best deal.

Correct Answer is : 5 fl oz bottle for $25

Q13Sarah wants to buy potatoes. Which is the best deal?

A. 1 kg for $5
B. 10 kg for $30
C. 5 kg for $20
D. 3 kg for $15

Solutions

Step: 1

If the unit price of an item is the lowest compared to others, then that item is said to be the best deal.

Step: 2

Unit price of potatoes = Price of all the kgs of potatoesNumber of the kgs of potatoes

Step: 3

In case of 5kg for $20, the unit cost = 205 = $4

Step: 4

In case of 3kg for $15, the unit cost = 153 = $5

Step: 5

In case of 10kg for $30,the unit cost = 3010 = $3

Step: 6

In case of 1kg for $5, the unit cost = 51 = $5

Step: 7

Therefore, 10 kg for $30 is the best deal.

Correct Answer is : 10 kg for $30

Q14Anna needs to buy some ribbons. The following deals are available at various stores. Choose the best deal.

A. $18 per 3 yd
B. $25 per 6 yd
C. $7 per 1 yd
D. $12 per 2 yd

Solutions

Step: 1

If the unit price of an item is the lowest compared to others, then that item is said to be the best deal.

Step: 2

Unit price of the ribbons = Price of all the yards of the ribbonsNumber of yards

Step: 3

In case of '$7 per 1yd', the unit cost = 71 =$7

Step: 4

In case of '$12 per 2 yd', the unit cost = 122 = $6

Step: 5

In case of '$25 per 6yd', the unit cost = 256 = $4.16

Step: 6

In case of '$18 per 3yd', the unit cost = 183 = $6

Step: 7

Therefore, '$25per 6 yd' is the best deal.

Correct Answer is : $25 per 6 yd

Q15Choose the best deal for apples.

A. $165.2 for 25 dozens
B. $142.72 for 28 dozens
C. $33.95 for 7 dozens
D. $30.56 for 5 dozens

Solutions

Step: 1

If the unit price of an item is the lowest compared to others, then that item is said to be the best deal.

Step: 2

Unit price of apple = Price of all dozens of applesnumber of dozens

Step: 3

In case of '$165.2 for 25 dozens', the unit cost = 165.225 = $6.608

Step: 4

In case of '$33.95 for 7 dozens', the unit cost = 33.957 = $4.85

Step: 5

In case of '$30.56 for 5dozens', the unit cost = 30.565 = $6.112

Step: 6

In case of '$142.72 for 28 dozens', the unit cost = 142.7228 = $5.09

Step: 7

Therefore, '$33.95 for 7 dozens' is the best deal.

Correct Answer is : $33.95 for 7 dozens

Solved Examples and Worksheet for Application of Proportions involving Unit Prices

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HighSchool Math