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## Math Problem Solutions - Set 2 (2019)

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%

``` 1.  6,500 ÷ 12 = 541.67
541.67 x 5.5 = \$2,979.19

2.  1,712 ÷ 90 = 19.02
19.02 x 19 = \$361.38

3.  405,000 x 3.5% = 14,175 (Down payment)
405,000 x 96.5% = 390,825 (Loan amount)
390,825 x 1.5% = 5,862.38 (Points)
\$14,175 (down payment) + \$5,862.38 (Points) = \$20,037.38

4.  319,000 x 5% = 15,950 (Gross commission)
15,950 ÷ 2 = 7,975 (50% of gross commission)
7,975 x 30% = 2,392.50 (Broker's share of listing side)
7,975 x 50% = 3,987.50 (Broker's share of selling side)
2,392.50 + 3987.50 = \$6,380

5.  100% - 4.5% (broker's commission) = 95.5% (Sellers required share)
280,000 (seller's required net) ÷ 95.5% = \$293,193.71

6.  325,000 ÷ 1,000 = 325
325 x \$6.00 = \$1,950

7.  216,000 x 6.25% = 13,500 (Annual interest)
13,500 ÷ 12 = \$1,125 (1 month interest)

8.  369,000 X 63% = 232,470 (Assessed value)
232,470 ÷ 100 = 2,324.7 (Units of 100)
2,324.7 x 3.81 = 8,857.11 (Annual taxes)
8,857.11 ÷ 360 = 24.60 (Daily tax rate)
24.60 x 19 days = \$467.40

9.  525,000 ÷ 2,750 = \$190.91

10.  100% + 12% = 112%

630,000 ÷ 112% = 562,500
562,500 ÷ 112% = 502,232.14
502,232.14 ÷ 112% = 448,421.55
448,421.55 ÷ 112% = 400,376.38

11.  125 x 70 = 8,750 x 4 floors = 35,000 sq. ft.
35,000 - 1,200 (Unusable space) = 33,800 (Rentable space)
20.75 x 33,800 = 701,350 (Annual rent)
701,350 ÷ 12 = \$58,445.83 (Monthly rent)

12.  25 acres x 24% = 6 Acres, open space
19 acres ÷ .5 = 38 Lots
38 lots x 175,000 = \$6,650,000

Option B   \$6,650,000
Option A   -5,000,000
\$1,650,000

13.                       _________________________________
/|   |                                 |
/ |   |                                 |
/  |   |                                 |20'
/   |   |                                 |
/    |   |                                 | __________
/     |50'|              (B)                ||          |
/      |   |                                 ||          |
/  (A)  |   |                                 ||   (C)    |
/        |   |                                 ||          |
/_________|   |_________________________________||__________|
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

\$116,141 ÷ 8,725 = \$13.31  Per square foot

If the neighbor bought the land, he would be buying the
triangular section (375 square feet)

\$13.31 x 375 = \$4,991.25

\$4,991.25  Cost to buy the land
-1,425.00  Cost to rebuild the fence
\$3,566.25  Difference

14.  1.87 x 43,560 (Square feet in an acre) = 81,457.2
3.55 x 81,457.2 = \$289,173.06

15.  1,640 x 12 = 19,680 (Annual interest)
19,680 ÷ 7% = 281,142.85 (Loan amount)
281,142.85 ÷ 85% = \$330,756.29 (Purchase Price)

16.  15,000 x 40% = 6,000 (Monthly expenses)
15,000 - 6,000 = 9,000 (Monthly net income)
9,000 x 12 = 108,000 (Annual net income)
108,000 ÷ 9% = \$1,200,000

17.  359,000 ÷ 135% = 265,925.92

18.  419,500 x 5% = 20,975 (Gross commission)
20,950 x 50% = 10,487.50 (Gross commission, Sam's office)
10,487.50 x 55% = \$5,768.13

19.  \$629,000 x 5% = \$31,450 Sales commission

Closing Costs
\$31,450  Commission
5,492  RTF
2,500  Concession
2,350  Legal and other
\$41,792

\$629,000 (sale price) - 41,792 = \$587,208
\$587,208 - 392,000 (mortgage payoff) = 195,208 Seller's Net

20.  100% - 7% = 93%

999,000 x 93% = 929,070
929,070 x 93% = 864,035.10
864,035.10 x 93% = 803,552.64
803,552.64 x 93% = 747,303.95
747,303.95 x 93% = 694,992.68

21.  14 x 16 = 224 sq. ft.
224 ÷ 9 = 24.89 sq. yds.
22.45 x 24.89 = \$558.78

22.  375,000 ÷ 1,000 = 375
6.00 x 375 = 2,250

7,586 + 628 = 8,214
8,214 ÷ 12 = 684.5

2,250 + 684.5 = \$2,934.50

23.  27.50 x 25,000 = 687,500

4,500,000 - 4,200,000 = 300,000
300,000 x 2.5% = 7,500

687,500 + 7,500 = \$695,000

24.  Present rent = 100%
Increased Rent = Present rent + 3% (103%) each year

\$2,350.00 x 103% = \$2,420.50
\$2,420.50 x 103% = \$2,493.12
\$2,493.12 x 103% = \$2,567.91
\$2,567.91 x 103% = \$2,644.95

25.  93,000 x 40% = 37,200 (Expenses)
93,000 - 37,200 = 55,800 (Annual net income)
55,800 ÷ 9.5% = \$587,368.42```
```26.  100 x 135 = 13,500 sq. ft.
13,500 x 18 = 243,000 cu. ft.```
```27.  \$495,000 x 80% = \$396,000
\$7.778 x 396 = \$3,080.09```   