A donation box can receive only cheques of ₹100, ₹250 and ₹1000. On the last day of the month, the box contained exactly 90 cheques totalling ₹42600. If the number of ₹1000 cheques was the maximum possible, what is the sum of the numbers of ₹100 and ₹250 cheques?
Answer and solution
Correct answer: 53
Solution
Let x=₹100 cheques, y=₹250, z=₹1000. $x+y+z=90$ and $100x+250y+1000z=\text{total}$. Solve system for valid integer solutions.