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Minimizing the difference between variables in a linear equation

Source:

August 11, 2019

linear equationalgebra

Problem Statement

A pen costs

\mathrm{Rs.}\, 13

and a note book costs

\mathrm{Rs.}\, 17

. A school spends exactly

\mathrm{Rs.}\, 10000

in the year

2018-19

to buy

\mathrm{Rs.}\, 10000

pens and

y

note books 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

\mathrm{Rs.}\, 10000

and buys

y

pens and

x

note books. How much more did the school pay?

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