# basic algebra question

Albert repays three installments, a, b and c, of a loan that he had taken for buying an electric heater. The total of the first installment and the second installment is 150. The total of the second installment and the third installment is 200. The total of the third installment and thrice the first installment is 250. What is the third installment?

it was asked in my interview for clerical work.

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Can you translate the given information into (three linear) equations? Could you then solve the system of equations? – David Mitra Jul 6 '12 at 15:39

So you have the system

\begin{align} a + b &= 150 \\ b + c &= 200 \\ 3a + c &= 250 \end{align}

And then you must solve it. Do you know how?

One way might be to subtract the second from the first to get $a + b - (b + c) = a - c = 150 - 200 = -50$, and then to add that to the third to get $a-c + (3a + c) = 4a= -50 + 250 = 200$. This says that $4a = 200$, so that $a = 50$. Then $b = 100$ and $c = 100$.

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how did u decide that one should substract equation 2 from 1 ... – user286035 Jul 6 '12 at 15:49
@user286035 Because doing so eliminates the variable $c$ – ItsNotObvious Jul 6 '12 at 15:59

Systematic elimination is usually the best way to go. Sometimes there are reasonable alternatives. For example, "add" all three equations. We get $4a+2b+2c=600$. But $2b+2c=400$, so $4a=200$, and therefore $a=50$.

Now easily we see that $b=100$ and therefore $c=100$.

Remark: Or perhaps the mental arithmetic is easier if from $4a+2b+2c=600$ we conclude that $2a+b+c=300$, so $2a=100$, and therefore $a=50$.

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i liked your way. The mental arith hint is very cool. But when to use which technique ? – user286035 Jul 8 '12 at 7:44
@user286035: For "real world" equations with usually messy coefficients, use systematic (Gaussian) elimination. In interview situations, hard to know, there likely is a trick. Exploit any symmetry. – André Nicolas Jul 8 '12 at 13:02