Wikipedia:Reference desk/Archives/Mathematics/2012 November 17

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November 17

applie mathematics

Test whether euation 2x-3y+7z=5,3x+y-3z=13,2x+19y-47z=32 are consistent or not. — Preceding unsigned comment added by 117.197.18.249 (talk) 07:23, 17 November 2012 (UTC)

Welcome to Wikipedia. Your question appears to be a homework question. I apologize if this is a misinterpretation, but it is our aim here not to do people's homework for them, but to merely aid them in doing it themselves. Letting someone else do your homework does not help you learn nearly as much as doing it yourself. Please attempt to solve the problem or answer the question yourself first. If you need help with a specific part of your homework, feel free to tell us where you are stuck and ask for help. If you need help grasping the concept of a problem, by all means let us know. Shadowjams (talk) 09:44, 17 November 2012 (UTC)

The wikipedia article you need is this: Linear Equation System. Bo Jacoby (talk) 11:29, 17 November 2012 (UTC).

installment calculation in simple interest problems

I am not able to understand installments problem in aptitude.
I have so many doubts on installments calculation.
I am going to ask those doubts by using below problem.
Problem: person X has taken $1000 from person Y with 10% intersest rate for 3 years.if person x wants to repay the amount in 3 equal annual installments,what will be the each installment?
My doubts:
Doubt1:
If x is each installment ,then does the below equation is correct or not?
1000+( (1000*10*3)/100)=3*x
I mean ,does the amount which is to be paid after 3 years based on simple interest is same as sum of three installments?
Doubt2:
Which one provide more money to lender either installments or normal simple interest method for three years?
Please give me the answer to the above problem and above doubts with detailed example.
I do not have any idea how interest is calculated in installments plan.
I hope you give solution to the above problem. — Preceding unsigned comment added by Phanihup (talk • contribs) 13:43, 17 November 2012 (UTC)

There are lenders who apply the simple interest formula to the full amount, then divide the total into three equal instalments as you have done above, but this is not the usual way to do the calculation. Reputable lenders usually apply the interest only to the reducing amount still owed. This is, in effect, a compound interest calculation to include interest on interest, but it will be cheaper for the borrower because they are not paying interest on amounts already repaid. The best way to do the calculation is usually to set up a model for the repayments on a spreadsheet, calculating the first year's interest, then an estimated repayment (R) (try your simple answer above), then calculate interest on the remaining balance for the second year, and so on, using "goal seek" on R to achieve a zero balance at the end. Let us know if you need help with this. Dbfirs 17:48, 17 November 2012 (UTC)

See Mortgage calculator#Monthly payment formula for the formula and its derivation. Duoduoduo (talk) 21:41, 17 November 2012 (UTC)

Thanks Duo, I knew there was a formula somewhere but failed to find it. It can easily be adapted for annual payments. Dbfirs 22:40, 17 November 2012 (UTC)

... as a check on your calculations (by either method), the yearly payments by the installment method should be just under £31.22 less per year than the simple interest method, so the simple interest method provides more money to the lender. Dbfirs 08:07, 18 November 2012 (UTC)

solve for x using log function 7^(x+3)=3^x

i get 4.59, just eant to ocnfirm my math is right. — Preceding unsigned comment added by 24.139.14.254 (talk) 18:46, 17 November 2012 (UTC) but i think the correct andwer is -4.59, but my i end my math with x=log7^2/log7/3 — Preceding unsigned comment added by 24.139.14.254 (talk) 18:57, 17 November 2012 (UTC)

$7^{x+3}=7^{x}\cdot 7^{3}=343\cdot 7^{x}$ Hope that helps. --CiaPan (talk) 20:39, 17 November 2012 (UTC)

As far as confirming your answers, just plug them back in and see if either is right. Neither one appears right, to me. Do you need further help ? StuRat (talk) 22:03, 17 November 2012 (UTC)

express given eqn in simplest form w/only positive exponents

((3^-7)p*(3^-4)p)/(3^8)p^3

i can't fully figure it out, this is my work:

((1/3^7)p*(1/3^4)p)/(3^8)p^3

(1/3^11)/(3^8)p^3

dunno what to do there. possible answers: a) 1/(3^19)p or b) (3^19)p or c) 1/(3^3)p or d) 3^3/p ... i say its c) or d) but cant figure out how to get the answer — Preceding unsigned comment added by 24.139.14.254 (talk) 22:22, 17 November 2012 (UTC)

Check your math when you go from ((1/3^7)p*(1/3^4)p)/(3^8)p^3 to (1/3^11)/(3^8)p^3. Duoduoduo (talk) 00:48, 18 November 2012 (UTC)