MAT7603 - Assignment 3: Comprehensive Problems on Ratios, Proportions

This assignment solution for MAT7603 focuses on problems involving ratios, proportions, and percentages. It includes setting up and simplifying ratios, finding unknown terms in proportions, and solving percentage-related questions involving discounts, sales increases, and tax calculations. Specific calculations cover percentage increases and decreases, determining original amounts after percentage changes, and currency conversions between US and Canadian dollars. The assignment provides detailed, step-by-step solutions to each problem, demonstrating the application of fundamental financial mathematics concepts. Desklib is a platform where students can find such solved assignments.

Assignment 3 Mat7603
Total Assignment 3 worth 54 marks = 5% of the overall course mark
A. Set up a ratio for each of the following and reduce to lowest terms: (1.5 marks each: Total 3
marks)
1. 15 hours to 3 days
15 :(3∗24)
Simplifying
15 :72
2. $40 per day for 12 employees for 14 days
Wage : Employees :time
40 :12 :14
Simplifying
20 :6 :7
B
A student spends 20 hours per week in classroom lecture time, 45 hour per week in individual
study time, and 5 hours per week travelling to and from school. What is the ratio that exists
between the three times? 2 marks.
Lec ture :Study :traversing
20 :45 :5
Simplifying
4 :9 : 1
C. Find the unknown term in the following proportions. (1.5 mark each: Total 3 marks)
1. n : 7 = 24 : 42
n=24/(42/7)
n =4
2. 4
5 : t = 1
3 : 5
8
t= ((1/3)/ (4/5))/(5/8)
t=2/3
D.

Material cost of a fan belt is five-eighths of the total cost, and labour cost is one-third of material
cost. If labour is $15, what is the total cost of the fan belt? 3 marks.
Cost of a fan belt=5 /8 of total cost
Labour=1/3 of material
Labour=$ 15
Materal=3∗15=$ 45
Total cost=45+15
Cost of fan belt=5 /8∗¿ $ 37.5
E. Compute each of the following: (1 mark each: Total 3 marks)
1. 0.02 % of 360=0.072
2. 0.9 % of 3600=0.0324
3. 3
4 % of 3600=2700
F. Use fractional equivalents to compute each of the following (round to a whole number
(integer)): (1 mark each: Total 2 marks)
1. 114 1/2 % of $460 = $526.7
2. 20 2/3 % of $35 = $7.23
G.
If total deductions on a yearly salary of $22,826 amounted to 15 1
3 %, how much was deducted?
2 marks.
15 1/3%,*$22,826=$3499.98
H.
Jim’s four sons were to share equally in a prize, each receiving $19 each. How much was the
total prize? 1 mark.
Let the prize be X
½ of x =$19
Therefore the price = $38

I.
A company’s bad debt is $16,425 which is 41/2% of sales. What were the company’s sales? 2
marks
41/2%=$16,425
100%=x
X=($16,425*1)/0.045=$365000
J. Answer each of the following questions: (3 marks each: Total 33 marks)
1. How much is $12 increased by 300%?
$12*300%=$36
2. What amount is 13 1
3 % less than $90?
13 1
3 % *90=$12
90−12=$ 78
3. The amount of $100 is what percent more than $40?
(100-40)/40=150%
4. What percent less than $600 is $594?
(600−594)/ 600=1 %
5. The number 110 is 20 1
2 % more than what number?
110*0.795=87.45
6. After an increase of 4%, the new amount is $139. What was the original amount?
104 %=$ 139
100= x
X =(1∗139)/1,04
¿ $ 133.65
7. A retail outlet is offered a discount of 4 1
2 % for payment in cash for an invoice of $912. If
it accepted the offer, how much was the cash payment?
Cash=100 %−4 1
2 %
Therefore=95.5 %∗912=870.96
8. Sales in July increased 15 % over June sales. If July sales amounted to $26,000, what
were June sales?
115 %=$ 26,000

100= x
X =22608.70
9. In Montreal, a car sold for $17,394 including tax of 13%. How many dollars was the tax
on the car?
17,394*0.13=2261-22
10. How many Canadian dollars can you buy for US$650 if one Canadian dollar is worth
US$0.7271?
650/0.7271=CDN $ 893.962
11. What is the price of gasoline per litre in CDN dollars if a US gallon of gasoline costs
US$3.12? One U.S. dollar is worth CDN$1.28 and one U.S. gallon is equivalent to 3.8
litres.
1 gallon=us $ 3.12
1 usd=CDN $ 1.28
Price oa gallon∈CDN $=3.12∗1.28=CDN $ 3.9936