Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$37$ Pens and $53$ pencils together cost Rs. $320$ while $53$ Pens and $37$ Pencils together cost Rs. $400$, Find the cost of a Pen and that of a Pencil.

So far I had done the following: Let cost of 1 Pen be $\mathrm{Rs}.x$

And let cost of $1$ Pencil be $\mathrm{Rs.}y$

So, equations will be:

$37 \cdot x + 53\cdot y = 320 \mathrm{-----} (1)$

$53 \cdot x + 37 \cdot y = 400 \mathrm{-----} (2)$

Now which formula I should apply to solve this linear equation in two variables.

Please Help

share|cite|improve this question
up vote 1 down vote accepted

Let $x$ be the cost of a pen, and let $y$ be the cost of a pencil.

Then $37x+53y=320$ and $53x+37y=400$. We have two linear equations in two unknowns. In principle this system of equations is routine to solve for $x$ and $y$, but it might be kind of messy.

But note the nice partial symmetry, and observe that $$(37x+53y)+(53x+37y)=90x+90y=90(x+y).$$

Remark: So now we know that the combined cost of a pen and pencil is $8$. So we are finished. But what about the individual costs? Note that $(53x+37y)-(37x+53y)=16(x-y)=400-320$. So $x-y=5$. Now we can easily find $x$ and $y$. For $(x+y)+(x-y)=2x=13$ and therefore $x=6.5$. It follows that $y=1.5$.

share|cite|improve this answer

x - cost of a pen y - cost of a pencil

37x + 53y = 320

53x + 37y = 400

you should be able to proceed. Try find value of x from one equality an set it up to second. then you have equality with y only, so can find an answer

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.