SOLUTION: A vendor sells 28 Whatszitand 35 Widgets. If the vendor makes a total of $463.96, what does the vendor charge for the Whatszit? What does the vendor charge for the Widget?

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Question 704701: A vendor sells 28 Whatszitand 35 Widgets. If the vendor makes a total of $463.96, what does the vendor charge for the Whatszit? What does the vendor charge for the Widget?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x = price of a Widget, in $
y = price of a Whatszit, in $
If the total sales were $463.96, we know that
35x%2B28y=463.96 --> 5x%2B4y=66.28 dividing both sides of the equal sign by 5
Without much information, we cannot say more.
We could solve for x as a function of y and get
x=%281%2F5%29%2866.28-4y%29
If the price has to be a whole number of cents (unlike the price per gallon for gasoline, which in the US seems to always end in 9/10 of a cent),
then the Widget must be priced at $0.04n where n is an integer such that 0%3C=n%3C=331.
The price of a widget could be $0.00. Maybe the vendor sells Whatszits at $16.57 each, and gives some Widgets for free with purchase of a Whatszit.
The price of a Widget could be $0.04, or $0.08, or ... or $13.20, or $13.24.
In between values would require y prices for the Whatszits with fractional cents, as in a $10.3325 price for a Whatszit if the price for a Widget was $4.99.