There are several different ways to approach a math problem and arrive at
the correct answer. The solutions provided here are believed to be the most basic
approach.
Remember:
To change a fraction to a decimal, divide the numerator by the denominator
Examples:
½ = 1 ÷ 2 = .5
¼ = 1 ÷ 4 = .25
To change a percentage to a
decimal, move the decimal two places to the left
Examples:
50% = .50 95% = .95
3% = .03
To change a decimal to a
percentage, move the decimal two places to the right Examples:
.5 = 50% .25 = 25%
1.50 = 150% |
PROBLEM 1
$1,548 ÷ 12 = $129 per month
$129 x 5.5 months = $709.50 or $710 to Ace
PROBLEM 2
$22,000 x .61 = $13,420
(Base) (Rate) (Part)
$89,000
-22,000
$67,000 Balance
$67,000 x .585 = $39,195
(Base) (Rate) (Part)
$13,420
+39,195
$52,615 Insurable
PROBLEM 3
$92,400 x .065 = $6,006 Gross Commission
(Base) (Rate) (Part)
$6,006 x .12 = $720.72 Listing Salesperson
(Base) (Rate) (Part)
$6,006.00
-720.72
$5,285.28
$5,285.28 x .45 = $2,378.38 To Scott
(Base) (Rate) (Part)
PROBLEM 4
$2,792.79 ÷ .45 = $6,206.20 "Balance"
(Part) (Rate) (Base) 88% of gross commission
$6,206.20 ÷ .88 = $7,052.50 "Gross Commission"
(Part) (Rate) (Base) 6½% of selling price
$7,052.50 ÷ .065 = $108,500 Sale price
(Part) (Rate) (Base)
PROBLEM 5
Base Rate Part
$18,500 x .05 = 925.00 x 1 year = 925.00
18,500 x .025 = 462.50 x 1 year = 462.50
18,500 x .015 = 277.50 x 10 years = 2,775.00
18,500 x .01 = 185.00 x 8 years = 1,480.00
$5,642.50 Total
PROBLEM 6
Base Rate Part
$75,000.00 x .06 = 4,500.00 Gross Commission
4,500.00 x .025 = 112.50 Office Manager
4,500.00 x .12 = 540.00 Listing Salesperson
3,847.50 x .35 = 1,346.63 Selling Salesperson
$4,500.00
- 112.50
- 540.00
$3,847.50 "Balance"
-1,346.63
$2,500.87 Broker
PROBLEM 7
INCOME EXPENSES
4 x 285 = $1,140
6 x 295 = 1,770 $3,484 Fuel
8 x 312 = 2,496 2,989 Maintenance
12 x 336 = 4,032 9,390 Taxes
$9,438 per month $15,863 per year
$9,438 x 12 = $113,256 Per year income
$113,256 Annual income
- 15,863 Annual expenses
$ 97,393 Net income
$97,393 x .035 = $3,408.76
(Base) (Rate) (Part)
$97,393 Net income
- 3,408 Commission
$93,984 Net to Capitalist
$93,984.24 ÷ 751,875 = .1249 or .125 or 12½% Return
(Part) (Base) (Rate)
PROBLEM 8
100% - 2½% = 97½% or .975
$82,500.00 ÷ .975 = $84,615.38 1 year ago
$84,615.38 ÷ .975 = $86,785.00 2 years ago
$86,785.00 ÷ .975 = $89,010.26 3 years ago
PROBLEM 9
Total frontage: 120'
Total investment: $6,000
Total price: 3 x 3,300 = $9,900
9,900 ÷ 120 = $82.50 per front foot
$9,900
x .06
$ 594 Commission
$9,900
- 594
$9,306 Net
$9,306 Net
-6,000 Investment
$3,306 Profit
$3,306 ÷ 6,000 = .551 or 55.1%
(Part) (Base) (Rate)
PROBLEM 10
100% Lower priced home
+125% Higher priced home
225% Total value
229,745 ÷ 2.25 = $102,108.88 Lower priced home
(Part) (Rate) (Base)
$229,745.00 Total
-102,108.88 Lower priced house
$127,636.12 Higher priced house
PROBLEM 11
100% + 3½ = 103½ or 1.035
28,800.00 ÷ 1.035 = $27,826.08 1 year ago
27,826.08 ÷ 1.035 = $26,885.10 2 years ago
26,885.10 ÷ 1.035 = $25,975.95 3 years ago
25,975.95 ÷ 1.035 = $25,097.53 4 years ago
PROBLEM 12
100% Invested
+15% Profit
155% Selling price
16,000 ÷ 1.15 = $13,913.04
PROBLEM 13
100 % Selling price
- 7½% Commission
92½% Net to seller
67,432.50 ÷ .925 = $72,900
(Part) (Rate) (Base)
PROBLEM 14
$69,302
+ 75
$69,377 Net commission
100 % Selling price
- 7¼% Commission
92¾% Net after commission
PROBLEM 15
100 x 200 = 20,000 Square feet
20,000 x $10 - $200,000 Purchase price
100' x $2.50 = $250 Sewer assessment
$200,000 Purchase price
250 Sewer
+ 1,000 Profit
$201,250 Net after commission
100% - 10% = 90% Net after commission
201,250 ÷ .90 = $223,611.11 Selling price
(Part) (Rate) (Base)
PROBLEM 16
OPTION B
10 (acres) x 4,840 = 48,400 Square yards total area
200 x 60½ = 12,100 Square yards each lot
48,400 ÷ 12,100 = 4 Lots
$16,000
x 4 Lots
$64,000
Option B yields $64,000
Option A yields -62,000
$ 2,000 Gain
PROBLEM 17
125 x 70 = 8,750 Square feet
8,750 x 3 (stories) = 26,250 Total Area
26,250 Total area
- 500 Walls
25,750 Rentable area
25,750 x .65 = $16,737.50 Per month
x 12
$200,850.00 Per year
PROBLEM 18
100% Original cost
+20% Increase
120% Current cost
$97,500 ÷ 1.20 = $81,250
(Part) (Rate) (Base)
PROBLEM 19
$114,000 Total
- 22,000 Lot
$ 92,000 House
HOUSE
100 %
- 2½%
97½% or .975
92,000 x .975 = $89,700.00 After 1 year
89,700 x .975 = $87,457.50 After 2 years
LOT
100%
+ 8%
108% or 1.08
22,000 x 1.08 = $23,760.00 After 1 year
23,760 x 1.08 = $25,660.80 After 2 years
$ 87,457.50 House
+ 25,660.80 Lot
$113,118.30 Total
PROBLEM 20
30,000 x .80 = $24,000 Loan
(Base) (Rate) (Part)
Monthly payment = 8.06 Per thousand dollars borrowed
$24,000 ÷ 1,000 = 24 Units of one thousand
$ 8.06
x 24
$193.44
PROBLEM 21
FIRST PROPERTY
33,000 x .80 = $26,400 Loan
$26,400 ÷ 1,000 = 26.4 Units of one thousand
$8.06 x 26.4 = $212.78 Payment
SECOND PROPERTY
45,000 x .75 = $33,750 Loan
$33,750 ÷ 1,000 = 33.75 Units of one thousand
$8.41 x 33.75 = $283.84
$283.84 Second property
-212.78 First property
$ 71.06 Difference
PROBLEM 22
37,500 x .095 = $3,562.50 Annual interest
(Base) (Rate) (Part)
3,562.50 ÷ 12 = $296.88 First month interest
PROBLEM 23
47,900 x .75 = $35,925 Loan
35,925 ÷ 1,000 = 35.925 Units of one thousand
$8.41 x 35.925 = $302.13 Monthly payment
1,325 ÷ 12 = $110.42 Monthly taxes
450 ÷ 36 = $ 12.50 Monthly insurance
$302.13 Principal & interest
110.42 Taxes
+ 12.50 Insurance
$425.05 Total
PROBLEM 24
$823 x 12 = $9,876 Annual interest
$9,876 ÷ .11 = $89,781.82 Loan
(Part) (Rate) (Base)
$89,781.82 ÷ .85 = $105,625.66 Sale price
(Part) (Rate) (Base)
PROBLEM 25
Closing occurs during a paid period so the seller gets
the credit. Seller gets the credit for the unused portion.
$1,136 ÷ 12 = $94.666 Per month
$94.666 x 7 months = $662.66
PROBLEM 26
$180 City tax
+240 School tax
$420 Total paid
$420 ÷ 12 = $35 Per month
$35 x 8½ months unused = $297.50 To seller
$118 county tax ÷ 12 = $9.833 Per month
$9.833 x 3½ months used = $34.42 To buyer
$297.50 Seller
- 34.42 Buyer
$263.08 To seller
PROBLEM 27
100%
+20% Appreciation
120% or 1.20
250 x 1.20 = 300 in 1982
300 x 1.20 = 360 in 1983
360 x 1.20 = 432 in 1984
PROBLEM 28
43,560 Square feet in an acre
x 1.87 Acres
81,457.2 Square feet
81,457.2 x .225¢ = $18,327.87
PROBLEM 29
$475 x 12 = $5,700 Minimum annual rent
$12,220 Total Rent
- 5,700 Minimum rent
$ 6,500 Extra rent
$6,500 ÷ .05 = $130,000 Business over $135,000
(Part) (Rate) (Base)
$135,000 Base volume
+130,000 Excess volume
$265,000 Total volume
PROBLEM 30
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/ | | | __________
/ |50'| (B) || |
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/ (A) | | || (C) |20'
/ | | || |
/_________| |_________________________________||__________|
15' 155' 20'
AREA
A) 15 x 50 = 750 ÷ 2 = 375 Square feet
B) 155 x 50 = 7,750 Square feet
C) 20 x 30 = 600 Square feet
375
1,750
+ 600
8,725 Total area
$16,141.25 ÷ 8,725 = $1.85 Per square foot
If the neighbor bought the land, he would be buying the
triangular section (375 square feet)
$1.85 x 375 = $693.75
$693.75 Cost to buy the land
-425.00 Cost to rebuild the fence
$268.75 Difference