Home Do You Qualify? Real Estate Industry News Tell Us What you Think Private Tutoring Report an Error

 Mortgage Rates

## Math Problem Solutions - Set 1

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 rightExamples:    .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
\$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

_________________________________
/|   |                                 |
/ |   |                                 |
/  |   |                                 |
/   |   |                                 |
/    |   |                                 | __________
/     |50'|              (B)                ||          |
/      |   |                                 ||          |
/  (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
```