You are making this into something algebraic when it is really just asking about the concept of a percentage. Let’s try thinking of it another way: A group of people have each won a different amount of money. Then, each gave $10 of their winnings to charity. They all gave the same AMOUNT. But who gave the biggest PERCENTAGE? If you won $100, then the $10 represents 1/10th of your winnings, or 10%. If you won $1000, then the $10 is only 1% of your winnings. If you won $20, then the $10 is half your winnings or 50%. The largest PERCENTAGE is that $10 out of the SMALLEST winnings.
Now in this problem, the smallest purchase that gets you the $10 is $50. So 10 out of 50 is the largest PERCENTAGE discount you can earn.
Then, it comes down to this: do you know how to find what percent $10 is out of $50? There are lots of ways to do this. The quickest is just know that 1/5 is 20%.
Slower method: divide 1 by 5, and then multiply by 100
An even slower method for students who are shaky at percents: set up the ratios “is/of” = “percent/100”
You get 10/50 = x/100 which you can cross multiply and divide.