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Algebra Math Olympiad PRMO USA Math Olympiad

Pen & Note Books Problem | PRMO-2019 | Question 16

Try this beautiful Problem from Algebra based on Pen & Note Books from PRMO 2019, Question 16. You may use sequential hints to solve the problem.

Try this beautiful Problem from Algebra based on Pen & Note Books from PRMO 2019.

Pen & Note Books – PRMO 2019, Problem 16


A pen costs Rs.13 and a notebook costs Rs.17. A school spends exactly Rs.10000 in the year 2017 – 18 to buy x pens and y notebooks such that $x$ and $y$ are as close as possible (i.e. $|x-y|$ is minimum). Next year, in $2018-19,$ the school spends a little more than Rs.10000 and buys y pens and x notebooks. How much more did the school pay?

  • $9$
  • $40$
  • $34$

Key Concepts


Algebra

Equation

multiplication

Check the Answer


Answer:$40$

PRMO-2019, Problem 16

Pre College Mathematics

Try with Hints


Given A pen costs Rs.\(13\) and a note book costs Rs.\(17\)

Nunber of pens \(x\) and numbers of notebooks \(y\)

According to question

\(13 x+17 y=10,000\) ……………………..(1)
\(17 x+13 y=10000+P\)………………….(2)

Where $\mathrm{P}$ is little more amount spend by school in $2018-19$.we have to find out the value of \(P\).Can you find out?

Can you now finish the problem ……….

Adding (1) & (2)

$x+y=\frac{20,000+P}{30}$

Subtract (1) form (2)

$x-y=\frac{P}{4}$

Let $P=4 a$
$\begin{aligned} \text { So, } x+y=& \frac{20,000+4 a}{30} \ &=666+\frac{10+2 a}{15} \end{aligned}$

Therefore \(a\)=\(10\)

Can you finish the problem……..

Since $P=4 a$ \(\Rightarrow P=40\)

So school had to pay Rs. 40 extra in 2018 – 2019

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