Math Problem Solutions - Set 2

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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%

 

 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.  205,000 x 3% = 6,150 (Down payment)
     205,000 x 97% = 198,850 (Loan amount)
     198,850 x 1.5% = 2,982.75 (Points)
     6,150 (down payment) + 2,977.50 (Points) = $9,132.75


 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

              $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


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.  75,600 + 285,000 = 360,600

     1,751.75 ÷ 91 days = 19.25 (Daily tax rate)
     19.25 x 20 days = 385

     360,600 + 385 = 360,985 (Sale price less broker's 5% commission)
     360,985 ÷ 95% = $379,984.21


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% = 694,992.67


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.  1,451 x 12 = 17,412 (Annual interest)
     17,412 ÷ 6.125% = $284,277.55


25.  93,000 x 40% = 37,200 (Expenses)
     93,000 - 37,200 = 55,800 (Annual net income)
     55,800 ÷ 9.5% = $587,368.42



      						

      						
							

      						

 

 

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