Deck 3: Ratio, Proportion, and Percent

Question 1

Carol, Clara and Nancy decide to buy LOTTO 649 tickets, agreeing to share any winnings in a ratio of : : , which is in the same ratio as they spent on tickets. If they end up winning $1147.00, calculate how much each should receive from the winnings.

Answer 1

Convert into fractions with the same denominators : : = : : the ratio is 10:15:12
total number of parts = 10 + 15 + 12 = 37
the value of each part is 1147 ÷ 37 = 31
Carol's share = 31 × 10 = $310.00
Clara's share = 31 × 15 = $465.00
Nancy's share = 31 × 12 = $372.00

Question 2

Solve: n:6 = 24:42

Answer 2

n:6 = 24:42
42n = 24 ∗ 6
n = = 3.42857

Question 3

Solve: 7:n = 35:21

Answer 3

7:n = 35:21 = 21 ∗ 7 = 35n
n = n = 4.2

Question 4

Solve: 4.2:x = 4.375:25.6

Question 5

Four beneficiaries are to divide an estate of $289 000 in the ratio : : : . How much should each receive?

Question 6

Sean, Paul and Wallis decide to buy a property, agreeing to share profit in a ratio of : : , which is in the same ratio as they spent on the property. If they end up making $20000.00, calculate how much each should receive from the sale of the property.

Question 7

Solve: 7:5 = x:40

Question 8

Set up a ratio to represent the following:
10 quarters to 12 dimes to 16 nickels

Question 9

Set up a ratio to represent the following:
one-half of an hour to 18 minutes

Question 10

Solve: 15:6 = 30:x

Question 11

The cost of a unit is made up of $7.25 direct material cost, $4.75 direct labor cost, and $3.50 overhead. What is the ratio that exists between the three elements of cost?

Question 12

The cost of operating the Repair Department is to be allocated to four production departments based on the floor space each occupies. Department A occupies 1100 m; Department B, 660 m; Department C, 880 m; and Department D, 440 m. If the July cost was $24 000, how much of the cost of operating the Repair Department should each production department absorb?

Question 13

At Upscale Corporation, direct selling expense amounted to $3500 while sales volume was $97 500 for last month. What is the ratio of direct selling expense to sales volume?

Question 14

The cost of a unit is made up of $120.00 direct material cost, $80.00 direct labor cost, and $20.00 overhead. What is the ratio that exists between the three elements of cost?

Question 15

Four beneficiaries are to divide an estate of $500 000 in the ratio : : : . How much should each receive?

Question 16

Manufacturing overhead is charged to three operating divisions on the basis of capital investment in the three divisions. If the investment is $10.8 million in the Eastern Division, $8.4 million in the Southern Division, and $17.4 million in the Far Eastern Division, how should manufacturing overhead of $888 000 be allocated to the three divisions?

Question 17

Lorraine, Estelle, and Frances own a business jointly and share profits and losses in the same proportion as their investments. How much of a profit of $14 500 will each receive if their investments are $14 000, $16 000, and $15 000 respectively?

Question 18

Students, A, B, and C occupy floor space of 50 m, 70 m, and 80 m, respectively. If the total rental for the space is $1000 per month, how much rent should student A pay?

Question 19

Departments A, B, and C occupy floor space of 310, 120 and 475 square meters respectively. If the total rental for the space is $38 225.00 per month, how much rent should be paid by Department B?

Question 20

Departments, A, B, and C occupy floor space of 60 m,90 m, and 300 m, respectively. If the total rental for the space is $125 200 per month, how much rent should Department C pay?

Question 21

Solve: :t = :

Question 22

Solve: 2.18:1.61 = k:4.4

Question 23

Solve: : = : t

Question 24

Solve: 1.15:2.30 = k:1.30

Question 25

A gas tank with a capacity of 245 L can be drained in twenty-five minutes. At the same rate, how many minutes will it take to drain a tank containing 176 L?

Question 26

Solve: : = t

Question 27

A Clothing company has found that, based on past experience, $17.50 must be spent on labour costs for every $13.25 spent on materials. If a budget of the year 2005 is set at $231 875.00 for materials, calculate the amount that must be budgeted for labour.

Question 28

Solve: 1.15:0.95 = k:1.19

Question 29

Gross profit for March was three-fifths of net sales, and net income was two-sevenths of gross profit. Net income was $14200.
a) What was the gross profit for March?
b) What were net sales for March?

Question 30

A manufacturing process requires $68.5 supervision cost for every 64 labor hours. At the same rate, how much supervision cost should be budgeted for 18 000 labor hours?

Question 31

Five-eighths of Jim Bernard's inventory was destroyed by water damage. He sold the remaining part, which was slightly damaged, for one-third of its value and received $5000.
a) What was the value of the destroyed part of the inventory?
b) What was the value of the inventory before the fire?

Question 32

Solve: : = : t

Question 33

Solve: y : = :

Question 34

Seven-eighths of Jim Whyte's inventory was destroyed by fire. He sold the remaining part, which was slightly damaged, for one-third of its value and received $1400.
a) What was the value of the destroyed part of the inventory?
b) What was the value of the inventory before the fire?

Question 35

Solve: 3.80:m = 10.8:8.10

Question 36

Solve: x: = 1 :

Question 37

Solve: 3.1:m = 1.4:1.9

Question 38

Mr. Duckworth owned 3/8 of a store. He sold 2/3 of his interest in the store for $37 000. What was the value of Mr. Duckworth's share of the store?

Question 39

The community of Oakville sets a property tax rate of $25.50 per $1000 assessed valuation. What is the assessment if a tax of $554 is paid on a property?

Question 40

Solve: 2.50:1.25 = k:4.4

Question 41

$36 is what percent of $14?

Question 42

27.5% of what amount is $28.63?

Question 43

Overhead content in an article is 37 1/2% of total cost. How much is the overhead cost if the total cost is $72?

Question 44

What is % of $12150?

Question 45

$170 is what percent of $80?

Question 46

A firm's bad debts of $7775 were 2 3/4% of sales. What were the firm's sales?

Question 47

165% of what amount is $370?

Question 48

The Canada Pension Plan premium deducted from an employee's wages was $131.59. If the premium rate is 2.925% of gross wages, how much were the employee's gross wages?

Question 49

What percent of $62.50 is $11.25?

Question 50

$901 is 31.2% of what amount?

Question 51

What percent of 0.14 is 0.035?

Question 52

What is 3/4% of $164.00?

Question 53

160% of what amount is $200?

Question 54

63 is what percent of 45?

Question 55

Overhead cost of a fan belt is three-eighths of total cost and labour cost is one-third of overhead cost. If labour cost is $15, what is the total cost of the fan belt?

Question 56

$189 is what percent of $4150?

Question 57

$750 is 33.3% of what amount?

Question 58

If total deductions on a yearly salary of $28 600 amounted to 16 2/3%, how much was deducted?

Question 59

225% of what amount is $310?

Question 60

$14.35 is 1/3% of what amount?

Question 61

What is 870 decreased by 21%?

Question 62

What is the rate percent if the base is 88 and the percentage is 65?

Question 63

166 2/3% of what amount is $280?

Question 64

The Canada Pension Plan premium deducted from an Peter's wages was $650.25. If the premium rate is 2.925% of gross wages, how much were Peter's gross wages?

Question 65

The amount of $2250 is what percent more than $2100?

Question 66

What amount is 8 1/3% less than $84?

Question 67

2 3/4% of what amount is $19.90?

Question 68

The amount of $123 is what percent less than $165?

Question 69

A property was sold for 250% of what the vendors originally paid. If the vendors sold the property for $218 000, how much did they originally pay for the property?

Question 70

The number 675 is 37 1/2% more than what number?

Question 71

$32 is what percent of $26?

Question 72

What is the rate percent if the base is 50 and the percentage is 35?

Question 73

What percent less than $90 is $81?

Question 74

$90 is 37 1/2% of what amount?

Question 75

In the last provincial election, 62 1/2% of the population of 994 800 was eligible to vote. Of those eligible, 33 1/3% voted.
a) What was the number of eligible voters?
b) How many voted?

Question 76

350% of $15.00 is what amount?

Question 77

$275 is 87 1/2% of what amount?

Question 78

How much is $27.40 increased by 237%?

Question 79

What amount is 16 2/3% less than $69?

Question 80

$75 is what percent of $50?