Question 1

Sam, Domenic, and Sal invested $100,000, $150,000 and $75,000 respectively in a business. The profits from last year were $80,000. How much of the profits should each partner receive?

Accepted Answer

The total investment is $325,000 ($100,000 + $150,000 + $75,000). The profit shares are proportional to the investments: Sam ($100,000/$325,000), Domenic ($150,000/$325,000), and Sal ($75,000/$325,000). Calculating these fractions of the $80,000 profit gives $24,615.38 for Sam, $36,923.08 for Domenic, and $18,461.54 for Sal.

Question 2

Susan, Lynda, and Monica opened a consignment dress shop. The partnership agreement states that the responsibilities for the provision of capital are in the ratio of 2.5: 3.75: 4.5. If the total investment in the business was $365,500, how much did each partner invest?

Accepted Answer

The total ratio is 2.5 + 3.75 + 4.5 = 10.75. The amount each partner invested is calculated by dividing their individual ratio by the total ratio and then multiplying by the total investment. Susan invested (2.5/10.75) * $365,500 = $85,000, Lynda invested (3.75/10.75) * $365,500 = $127,500, and Monica invested (4.5/10.75) * $365,500 = $153,000.

Question 3

Jane, Lynda, and Ginny run a consignment dress store. The partnership agreement states that the profits are distributed according to the hours each works in the store. For the month of July, profits are $8,500. The hours worked by Jane, Lynda and Ginny are 170, 190, and 200 respectively. How should the month's profits be allocated?

Accepted Answer

The total hours worked are 170 + 190 + 200 = 560 hours. The profit per hour is $8,500 / 560 = $15.17857. Therefore, Jane's share is 170 * $15.17857 = $2,580.36, Lynda's share is 190 * $15.17857 = $2,883.93, and Ginny's share is 200 * $15.17857 = $3,035.71.

Question 4

Based on past experience, a production process requires 15 hours of direct labour and 2 assemblers for every $450 of raw materials. If the company has budgeted for $33,750 worth of raw materials, how many hours of direct labour and how many assemblers will the company require?

Accepted Answer

Since the production process requires 2 assemblers for every $450 of raw materials,
Number of assemblers = (Raw materials budgeted for / $450 per assembler)
= 33750 / 450 = 75 assemblers

Also, from the past experience, it is known that 15 hours of direct labor is required for the production process.
Therefore, Total hours of direct labour required = 75 * 15
= 1125 hours

Hence, the company will require 1125 hours of direct labour and 150 assemblers. Option C is the correct answer.

Question 5

The current exchange rates show that C$1.00 = US$0.9672. If you have $120 Canadian dollars, what is the equivalent amount in US dollars?

Accepted Answer

To find the equivalent amount in US dollars, multiply the amount in Canadian dollars by the exchange rate: $120 * 0.9672 = US$116.06.

Question 6

A college allows parking permits for students in the ratio of 5.5 students to a parking permit. The college currently has 11,000 students. The student council did a survey and found that the ratio should be 4:1. The college has agreed to add the extra parking spaces. How many more spaces are required to meet the 4:1 ratio?

Accepted Answer

The answer of A college allows parking permits for students...

Question 7

A punch recipe calls for orange juice, ginger ale, and vodka to be mixed in the ratio of 4.5:2.5:1. How much orange juice and vodka should be mixed with 2-litre bottle of ginger ale?

Accepted Answer

The total ratio is 4.5 (orange juice) + 2.5 (ginger ale) + 1 (vodka) = 8. The ginger ale part is 2.5/8 of the total mix. If 2 litres of ginger ale represents 2.5 parts, then 1 part equals 2/2.5 = 0.8 litres. Therefore, orange juice (4.5 parts) should be 4.5 * 0.8 = 3.6 litres, and vodka (1 part) should be 1 * 0.8 = 0.8 litres.

Question 8

Sam, Domenic, and Sal invested $100,000, $125,000 and $150,000 respectively in a business. In order to expand a further investment was required. Sal invested $200,000. If the other partners agreed to provide capital in the same ratio as the initial investment, how much did Sam and Domenic invest?

Accepted Answer

The total initial investment was $375,000 ($100,000 + $125,000 + $150,000).
After Sal's investment, the total investment became $725,000 ($375,000 + $200,000 + $150,000).
Sam's initial investment was 100,000/375,000 of the total initial investment ratio, which simplifies to 4/15. 
Domenic's initial investment was 125,000/375,000 of the total initial investment ratio, which simplifies to 5/15 or 1/3.
Therefore, Sam should invest 4/15 of the additional $200,000, which is 4/15 x $200,000 = $53,333.33.
Domenic should invest 1/3 of the additional $200,000, which is 1/3 x $200,000 = $66,666.67.
Hence, Sam and Domenic should invest $133,333.33 and $166,666.67 respectively.

Question 9

Solve the proportion:

Accepted Answer

The given proportion can be written as:
11/TB4281 = 27.5/50
Cross-multiplying, we get:
11 x 50 = 27.5 x TB4281
TB4281 = (11 x 50)/27.5 = 20
Therefore, the proportion is 11:20, which is option C.

Question 10

During 1999, Acme Company's total overhead of $685,000 was allocated as follows: 18% to division A, 42% to division B, and the remainder to division C. What is the ratio of the overhead in division A to the overhead in division B to the overhead in division C in the lowest terms?

Accepted Answer

First, we need to find the amount of overhead allocated to division C.

18% + 42% = 60% of the overhead is allocated to divisions A and B, so the remainder (100% - 60% = 40%) is allocated to division C.

To find the amount of overhead in each division, we can multiply the total overhead by the percentage of overhead allocated to each division:

Division A: 0.18 × $685,000 = $123,300

Division B: 0.42 × $685,000 = $287,700

Division C: $685,000 - $123,300 - $287,700 = $274,000

Next, we need to simplify the ratio of overhead in each division. We can do this by dividing each amount of overhead by the greatest common factor (GCF) of all three amounts, which is $1,000.

Division A: $123,300 ÷ $1,000 = 123.3
Division B: $287,700 ÷ $1,000 = 287.7
Division C: $274,000 ÷ $1,000 = 274

The simplified ratio is 123.3 : 287.7 : 274, which can be further simplified by dividing each amount by 0.3:

Division A: 123.3 ÷ 0.3 = 411
Division B: 287.7 ÷ 0.3 = 959
Division C: 274 ÷ 0.3 = 913.3

So the lowest terms ratio of overhead in each division is 411 : 959 : 913.3, which simplifies to 9 : 21 : 20. Therefore, the answer is choice B.

Question 11

Sam, Domenic, and Sal invested $200,000, $125,000 and $150,000 respectively in a business. In order to expand a further investment was required. Sal invested $200,000. If the other partners agreed to provide capital in the same ratio as the initial investment, how much did Sam and Domenic invest?

Accepted Answer

The total initial investment was $475,000 ($200,000 + $125,000 + $150,000). After Sal's additional investment of $200,000, the total investment becomes $675,000.

To find out how much Sam and Domenic should invest, we need to figure out the ratio of their initial investment to the total initial investment:

Sam's ratio = $200,000 / $475,000 = 0.421 (rounded to three decimal places) 
Domenic's ratio = $125,000 / $475,000 = 0.263 
Sal's ratio = $150,000 / $475,000 = 0.316

Since Sam and Domenic should invest in the same ratio, we can set up a proportion:

0.421/0.263 = (x + y)/$200,000

where x is Sam's additional investment and y is Domenic's additional investment.

Solving for x + y, we get:

(x + y) = $200,000 x (0.421/0.263) = $321,637

So, Sam and Domenic together should invest $321,637. To find out how much each should invest, we can use the same ratio:

Sam's investment = 0.421 x $321,637 = $135,664 (rounded to the nearest dollar) 
Domenic's investment = 0.263 x $321,637 = $84,973 (rounded to the nearest dollar)

Therefore, Sam and Domenic should invest $135,664 and $84,973 respectively. The answer is choice C.

Question 12

Mr. Malik is considering a larger house in the same area. Currently the taxes on his $250,000 home are $3,000 per year. If he expects that the taxes on other homes in the area are in the same ratio as the assessed values, what amount of taxes can Mr. Malki expect to pay on a house assessed at $300,000?

Accepted Answer

Since the taxes are directly proportional to the assessed value, we can set up a proportion as follows:

$250,000 : $300,000 = $3,000 : x

Simplifying this proportion, we get:

5 : 6 = 3,000 : x

Cross-multiplying, we get:

5x = 18,000

Dividing both sides by 5, we get:

x = $3,600

Therefore, Mr. Malik can expect to pay $3,600 per year in taxes on a house assessed at $300,000. Choice (B) is the correct answer.

Question 13

Solve the proportion:

Accepted Answer

The answer of Solve the proportion: 
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Question 14

Solve the proportion:

Accepted Answer

The answer of Solve the proportion: 
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Question 15

Solve the proportion:

Accepted Answer

The answer of Solve the proportion: 
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Question 16

Express the ratio 0.25: 1.40: 8.50 in its lowest terms:

Accepted Answer

The answer of Express the ratio 0.25: 1.40: 8.50 in...

Question 17

Nitin and Sam have invested in a partnership in the ratio of 3:5. If Sam adds another $10,000 to the business, how much should Nitin invest in order to maintain the same ratio?

Accepted Answer

Let Nitin's investment be 3x and Sam's investment be 5x.
After Sam adds $10,000, the new total investment becomes 3x+5x+10,000 = 8x+10,000.
To maintain the same ratio of 3:5, Nitin's new investment should be 3/5 of the total investment.
So, Nitin's new investment should be (3/5)(8x+10,000).
Now we can set up an equation:
3x = (3/5)(8x+10,000)
Multiplying both sides by 5:
15x = 3(8x+10,000)
15x = 24x + 30,000
9x = 30,000
x = 3,333.33
So Nitin's new investment should be (3/5)(8(3,333.33)+10,000) = $6,000.

Question 18

Kuldip and Jane invested $35,000 and $55,000 respectively in a partnership. Kuldip added another $20,000 and Jane wants to add enough to maintain their investments in the original ratio. How much should Jane invest in order to maintain the same ratio?

Accepted Answer

The original investment ratio is:
Kuldip : Jane = 35,000 : 55,000 = 7 : 11 
Kuldip added $20,000 to the partnership, so the new total investment is $35,000 + $20,000 = $55,000 for Kuldip. 
To maintain the 7:11 investment ratio, Jane needs to invest:
$55,000 * (11/7) - $55,000 = $31,429. 
Therefore, Jane should invest $31,429 so that the investment ratio remains the same.

Question 19

Aaron, Luc and Isaac invested in a business in the ratio of 3.5: 5: 7.5. The factory that they leased requires renovations of $125,000. If the partners want to maintain their investments in the business in the same ratio, how much should each partner pay for the renovations?

Accepted Answer

First, we need to find the total ratio, which is 3.5 + 5 + 7.5 = 16.

Next, we need to find the amount of money each partner would invest in the business. We do this by dividing their investment ratio by the total ratio:

Aaron: (3.5 / 16) x 100 = 21.875%
Luc: (5 / 16) x 100 = 31.25%
Isaac: (7.5 / 16) x 100 = 46.875%

Now, we can use these percentages to find out how much each partner should pay for the renovations:

Aaron: 21.875% x $125,000 = $27,343.75
Luc: 31.25% x $125,000 = $39,062.50
Isaac: 46.875% x $125,000 = $58,593.75

Therefore, the answer is E, with Aaron paying $27,343.75, Luc paying $39,062.50, and Isaac paying $58,593.75.

Question 20

A gym club membership costs $499 for two years. A member may cancel at any time and a refund less a $75 administration fee will be issued. The notice of cancellation must be received by the 15^th of the month in order for the cancellation to be effective for the following month. Najib purchased a membership on March 1^st last year, and decided to cancel it on June 10^th of this year. How much of a refund will Najib receive?

Accepted Answer

The answer of A gym club membership costs $499 for...

Quiz 3: Ratios and Proportions

Sam, Domenic, and Sal invested $100,000, $150,000 and $75,000 respectively in a business. The profits from last year were $80,000. How much of the profits should each partner receive?

Susan, Lynda, and Monica opened a consignment dress shop. The partnership agreement states that the responsibilities for the provision of capital are in the ratio of 2.5: 3.75: 4.5. If the total investment in the business was $365,500, how much did each partner invest?

Based on past experience, a production process requires 15 hours of direct labour and 2 assemblers for every $450 of raw materials. If the company has budgeted for $33,750 worth of raw materials, how many hours of direct labour and how many assemblers will the company require?

The current exchange rates show that C$1.00 = US$0.9672. If you have $120 Canadian dollars, what is the equivalent amount in US dollars?

A punch recipe calls for orange juice, ginger ale, and vodka to be mixed in the ratio of 4.5:2.5:1. How much orange juice and vodka should be mixed with 2-litre bottle of ginger ale?

Sam, Domenic, and Sal invested $100,000, $125,000 and $150,000 respectively in a business. In order to expand a further investment was required. Sal invested $200,000. If the other partners agreed to provide capital in the same ratio as the initial investment, how much did Sam and Domenic invest?

Solve the proportion:

During 1999, Acme Company's total overhead of $685,000 was allocated as follows: 18% to division A, 42% to division B, and the remainder to division C. What is the ratio of the overhead in division A to the overhead in division B to the overhead in division C in the lowest terms?

Sam, Domenic, and Sal invested $200,000, $125,000 and $150,000 respectively in a business. In order to expand a further investment was required. Sal invested $200,000. If the other partners agreed to provide capital in the same ratio as the initial investment, how much did Sam and Domenic invest?

Solve the proportion:

Solve the proportion:

Solve the proportion:

Express the ratio 0.25: 1.40: 8.50 in its lowest terms:

Nitin and Sam have invested in a partnership in the ratio of 3:5. If Sam adds another $10,000 to the business, how much should Nitin invest in order to maintain the same ratio?

Kuldip and Jane invested $35,000 and $55,000 respectively in a partnership. Kuldip added another $20,000 and Jane wants to add enough to maintain their investments in the original ratio. How much should Jane invest in order to maintain the same ratio?

Aaron, Luc and Isaac invested in a business in the ratio of 3.5: 5: 7.5. The factory that they leased requires renovations of $125,000. If the partners want to maintain their investments in the business in the same ratio, how much should each partner pay for the renovations?