DAT Achiever Math question

[MelissaB]

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Hi, I just found this very helpful site and my DAT is on Friday. I was wondering if anybody can help me with a math question that I'm stuck on. It's from the DAT Achiever test 1, #34 and a similar question test 2, #34:

Each DVD movie on sale is either $9 or $4 off its original retail price. If the total amount of discount shown on a receipt had been $106, what would have been the maximum number of $9-discounted-DVDs selected off the shelves by the receipt holder?

I have 9x + 4y = 106. now what? I have 2 unknowns and only 1 equation.
According to the solution, x could be 10, 6, 2 and y could be 4, 13, 22. How did they come up with these numbers besides trying every single one? 😕
Thanks for your help!

 

[seoul]

Just as each copy of DVD constitutes one complete set of item, so can you assign x and y with complete/whole/integer numbers alone. (No fractions, decimals, ... , let alone the negative numbers)

You've been asked for the highest possible integer of x. The wisest way to get to this is to begin assigning the value of y from its smallest possible value (i.e. y = 0, 1, 2, 3, 4, ...). And you'll easily notice that y = 4 is the smallest possible number to yield the first integer for x, where 10 turns out to be the largest possible integer in this case, so that 9(10) + 4(4) = 106. And you can forget about the rest... 🙂

 

[MelissaB]

Thanks Seoul, that was very helpful. 🙂