Real Life Math Problem

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Bill1860

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Oct 4, 2012
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Problem:
A condominium building has three units. The ownership for 'unit one' is 32 precent. The ownership for 'unit two' is 34 precent. The ownership for 'unit three' is 34 precent.

If the condominium does an assessment for each unit in proportion to ownership to paint the building, and units two and three each pay $5000, how much should unit one contribute?

==================================================
Is this the correct answer?
[1] 34 + 34 + 32 = 100 percent ownership
[2] unit one owes 2 percent less than the other units
[3] 2 percent of $5000 is $100 (2% X $5000 = .02X$000 = $100)
[4] unit one owes $4900 to paint the house ($5000 -$100 =$4900)


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A friend said the answer was $4706? I have no clue how they got that answer.
 
Bill1860 said:
Problem:
A condominium building has three units. The ownership for 'unit one' is 32 precent. The ownership for 'unit two' is 34 precent. The ownership for 'unit three' is 34 precent.

If the condominium does an assessment for each unit in proportion to ownership to paint the building, and units two and three each pay $5000, how much should unit one contribute?

==================================================
Is this the correct answer?
[1] 34 + 34 + 32 = 100 percent ownership
[2] unit one owes 2 percent less than the other units
[3] 2 percent of $5000 is $100 (2% X $5000 = .02X$000 = $100)
[4] unit one owes $4900 to paint the house ($5000 -$100 =$4900)


===========
A friend said the answer was $4706? I have no clue how they got that answer.
Click to expand...

5000 * 32/34 = 4705.88
 
Bill1860 said:
Problem:
A condominium building has three units. The ownership for 'unit one' is 32 precent. The ownership for 'unit two' is 34 precent. The ownership for 'unit three' is 34 precent.

If the condominium does an assessment for each unit in proportion to ownership to paint the building, and units two and three each pay $5000, how much should unit one contribute?

==================================================
Is this the correct answer?
[1] 34 + 34 + 32 = 100 percent ownership
[2] unit one owes 2 percent less than the other units
[3] 2 percent of $5000 is $100 (2% X $5000 = .02X$000 = $100)
[4] unit one owes $4900 to paint the house ($5000 -$100 =$4900)


===========
A friend said the answer was $4706? I have no clue how they got that answer.
Click to expand...
Let's first show that your friend was correct although the answer can be approximated more closely.

\(\displaystyle 5,000.00 + 5,000.00 + 4,705.88 = 14,705.88.\)

\(\displaystyle 34\%\ of\ 14,705.88 = 4,999.9992 \approx 5,000.00.\)

\(\displaystyle 32\%\ of\ 14,705.88 = 4,705.8816 \approx 4,705.88.\)

Your answer does not work.

\(\displaystyle 5,000 + 5,000 + 4,900 = 14,900,\ but\ 0.34 * 14,900 = 5,066 \ne 5,000.\)

Why did you get the wrong answer?

Because you were applying 32% to the 5,000, not the total cost. The differential of 2% applies to the total cost, not to 34% of the cost.

How do you get the right answer? Algebra.

\(\displaystyle Let\ x = total\ cost.\)

\(\displaystyle 0.34x = 5,000. \implies x = \dfrac{5,000}{0.34} \approx 14,705.88.\)

\(\displaystyle 0.32 * 14,705.88 \approx 4,705.88.\)
 
Last edited:
Yet another way: Units 2 and 3 account for 34% each so a total of 68%. If the total amount due from all three apartments is A then .68A+ 32A= A. Since .34A= 5000, A= 5000/.34= 14706. That leaves 4706 for unit 1 to pay- and, of course, .32(14706) = 4705.92 which rounds to $4706.
 
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