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maksim [4K]
3 years ago
10

the larger of two number is nine more than four times the smaller number. the sum of the two numbers is fifty-nine. find the two

numbeers
Mathematics
1 answer:
VLD [36.1K]3 years ago
4 0
This is solved by setting up two equations and then using one to answer the other.
The first step (use what is given to set up the two separate equations)
We are looking for two numbers, let us call them X and Y. 
We are told that X + Y = 59
 We are also told that (9 more than) 9+ (4times the smaller number) 4Y is the bigger number X
Then we combine that into 9+4Y=X
so we now have two separate equations and we can use one to solve the other. Everywhere we have X in the first equation, we will fill in with the second equation
(9+4Y) +Y = 59    [then combine like terms]
9+5Y=59            [subtract 9 from both sides]
5Y=50                   [divide both sides by 5 to isolate the Y]
Y=10                      [now plug this into either equation to solve for X]
9+4(10)=X
9+40=X
<u><em>49=X and 10=Y</em></u>
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<h3>What is closing cost?</h3>

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A lender estimates the closing costs on a home loan will be 3.75% of the loan amount of $120,000.  Thus, the estimate closing cost is,

C_{ec}=\dfrac{3.75}{100}\times120000\\C_{ec}=4500

The actual closing costs are listed below.  

  • Loan origination   $300
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  • Attorney’s fees     $1,250
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  • Recording fees     $125
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The total annual cost is,

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Total annual cost is $300 more than the estimate closing cost. In the percentage form,

p=\dfrac{4800-4500}{4500}\times100\\p=6.66\%

Thus, the lender’s good faith estimate is that he made a poor estimate; it was off by more than 0.5% of the actual closing costs.

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