SOLVED QUESTIONS
1. Reduce the following fractions to the lowest terms.
27/27 = 1 and 135/27 = 5
27/135 = 1/5
Convert the following mixed number into decimal form.
4+2/5 = 22/5
= 4.4
Simplify the following:
1- [ XXXXXXXXXX-0.22)]
= 1- [ XXXXXXXXXX)]
= XXXXXXXXXX
= 0.6607
Change the following percent into decimals.
200%
200/100 = 2
What is a salesperson’s commission on net sales of $16,244 if the commission is paid on
a sliding scale of 8 ¼% on the first $12,000, and 11.5% on any additional net sales?
= Net sales are $16,244
8 ¼% on the first $12,000
11 ½% on any additional net sales
8 ¼% *12000 = 0.0825*12000 = $990.00
11 ½%*4244 = 0.115*4244 = $488.06
XXXXXXXXXX = $1,478.06
The salesperson’s commission on net sales of $16,244 is $1478.06
Express the following as a percent:
0.04
0.04 × 100 = 4
The basic pay categories, hourly rates of pay and the number of employees in each category of a company are shown below:
Category
Hourly pay
No. of employees
Superviso
$40
2
Assistants
$16
10
Helpers
$14
10
TOTALS
$70
22
What is the average rate of pay per employee?
$40 *2 = $80
$16*10 = $160
$14*10 = $140
XXXXXXXXXX = $380
380/30 employees = $17.273
The average rate of pay is $17.27 per employee.
John invested $12,000 in a business on January 1 and an additional $2400 on April 1. He withdraws $1440 in June 1 and invested $2880 on October 1. What was Brent’s average monthly investment balance for the year?
Date XXXXXXXXXXChange XXXXXXXXXXBalance * XXXXXXXXXXMonths invested = XXXXXXXXXXValue
January 1 XXXXXXXXXX12000 * XXXXXXXXXX = $36,000
April 1 XXXXXXXXXX XXXXXXXXXX14400 * XXXXXXXXXX = $28,800
June 1 XXXXXXXXXX XXXXXXXXXX12960 * XXXXXXXXXX = $51,840
October XXXXXXXXXX XXXXXXXXXX15840 * XXXXXXXXXX = $47,520
XXXXXXXXXXTOTALS 12 $164,160
XXXXXXXXXXAverage monthly investment balance = total weighted value/number of months
= $164.160/12 = $13,680.00
Last week Lisa had gross earnings of $ XXXXXXXXXXLisa receives a base salary of $375 and a commission on sales exceeding her quota of $5000. What is her rate of commission if her sales were $6560?
Lisa’s gross earning last week = $441.30
Lisa’s base salary = $ 375.00
Lisa’s sales last week = $6560.00
$441.30-$375.00 = $66.30 commission
$6560.00/$5000.00 = 0.0425
Lisa’s rate of commission is 4.25%
A store located in Vancouver, B.C., sells a computer for $1800 plus GST and PST. If the same model is sold at the same price in a store in Toronto, Ontario, what is the difference in the prices paid by consumers in the two stores?
Computer sold in Vancouver, BC for $1800 plus GST and PST 5% and 7%
Computer sold in Toronto, ON for $1800 plus HST 13%
BC: $1800+12% = XXXXXXXXXXtaxes = $ 2,016 paid in BC
ON: $1800+13% = $ XXXXXXXXXXtaxes = $2034 paid in ON
$2016-$2034 = $18
Walmart sold a stereo set during a sale for $500. Determine the regular selling price of the set if the price of the set had been reduced by one-third of the original regular selling price.
x-1/3x = $500
2/3x = $500
(3)2/3x = $500(3)
2x = 1500
x = 1500/2 =750
x = 750
A wood piece 100-centimeter long is cut into two pieces so that the longer piece is 10 centimetres longer than twice the length of the shorter piece. What is the length of the longer piece?
x+ (2x+10) = 100
3x = 100-10
3x = 90
x = 90/3
x = 30
30+70 = 100
Simplify:
a. (-18x2y)/(3x)
- 18x2y/3x = -6xy
. (x-4) (x XXXXXXXXXXx-3) (x+2)
x2-x-4x+4-4x2 +4x+24
x2-4x2-5x+4x+4+24
-3x2 – x +28
Simplify:
XXXXXXXXXX
XXXXXXXXXX5)
1-3125 = -3124
Solve each of the following:
a. 2x+0.03x = 255
2.03 x = 255
x = 255/2.03
x = XXXXXXXXXX
. 8x-6-2x = 14+4x-6
8x – 6 + 6 – 2x – 4x = 14
8x – 2x – 4x = 14
2x = 14
x = 14/2 = 7
Set up a ratio for each of the following and reduce to lowest terms.
a. 14 hours to 2 days
= 14 hours/48 hours =7 hou
24 hours
. 60 $ per day for 12 employees for 18 days
Labour per day: Employees: Days
= $60 : 12 : 18
= 10: 2 : 3
The cost of a unit is made up of $6.25 material cost, $4.75 labour cost, and $3.25 overhead. What is the ratio that exists between the three elements of cost?
6.25: 4.75: 3.25 = 625: 475: 325
= 25: 19: 13
Solve:
a:6 =20:40
(a/6) = (20/40)
a = (20X6)/40 = 3
Material cost of a computer is five-eighths of total cost, and labour cost is one-third of material cost. If labour cost is $20, what is the total cost of the computer?
Let material cost be x
1/3 = 20/x
(1/3) x = 20
x = 20*3 = 60
Let total cost be y
5/8 = 60/y
5y = 8(60)
y = 96
Total cost is $96
Your utility bill for April is $170. If you pay after the due date, a late payment penalty of $7.72 is added. What is the percent penalty?
Bill = $170
Penalty = 7.72/170 = 0.045
Percent penalty = 45%
A
okerage firm charges a fee of 1 ¼%. If its fee on a stock purchase was $400, what was the amount of the purchase?
Let the amount of the purchase be x$
1 ¼% of x = 400
.0125 x = 400
x = 32,000
The amount of the purchase was $32,000
In Ontario, car was sold for $14,950 including 15% HST. How much was the sales tax on the car?
Let the price of the car be $x
x + %15of x = 14,950
x + 0.15x = 14,950
1.15x = 14,950
x = 14950/1.15
x = $13,000
sales tax = 15% of 13,000 = 1,950
Sales tax was $1,950
How many Canadian dollars can you buy for US$518 if one Canadian dollar is worth US$0.74?
1/0.74 = X/518
X = 518/0.74 = 700
C$ 700
John annual incomes for 2015 and 2016 were 60,000 and 70,000 respectively. Given that consumer price index for the two years was 110.5 and 109.4 respectively. Compute John’s real income for 2015 and 2016.
2015 = 60000/110.5*100 = $54,298.64
2016 = 70000/109.4*100 = $63,985.37
The appraised value of a property has increased since it was purchased by the present owner. The purchase price of the property was $160,000, its appraised value at that time. How much is the cu
ent appraised value?
Appraised value:
= $160,000 + $160,000 x
= 160, XXXXXXXXXX,800
Appraised value = $258,800
Media Marketing of Toronto, offers a two-day accommodation coupon for a Hilton resort in Alberta at a promotion price of C$216. If the exchange rate is C$1.18 per U.S dollar, what is the value of the coupon in U.S. dollar?
216 /1.18 = $183.05
The coupon has a value of US$ 183.05
Solve each of the following systems of equations and check your answer.
a. 2X+5y = 0
2X+2y = 6
2X+5y = 0
2X+2y = 6
2X+5y = 0 (1)
2X+2y = 6 (2)
Multiply eq (2) by -1 and add to eq (1) to eliminate X
3y = - 6
Y = -6/3 = -2
2X+5y = 0
2X+5(-2) = 0
2X-10 = 0, x = 10/2 = 5
X = 5, Y = - 2
Check:
In