The Secretary of the School Puzzle Solvers Society sends the Treasurer to the stationery shop to buy as many ballpoint pens and notebooks as she can lay her hands on. The price of a pen is $e2.45$ and the price of a notebook is $e1.60$. On her return, the Treasurer says that she spent a total of $e419.45$. (a) Write out the above information using a linear Diophantine equation and explain the meaning of any symbols you use. (b) Find all possible solutions to the Diophantine equation that reveal how many pens and how many notebooks the Treasurer may have bought
I have so far got the equation $$245x+160y=41945$$
I have found the $$\gcd(245,160) = 5$$
I am now trying to roll back but that confuses me.
I let $5 = 75-7\cdot 10$
Am i on the right track?