A man sold one sort of oranges at 5 for $2, and another sort at 16 for $12. If he had sold them all at $0.5 each, he would have received $2 less. If he had sold all at 3 for $2, he would have received $18 more. How many of each sort did he sell?
Let's call the amounts
What he did can be translated into:
The second option can be translated into:
The last option would be:
If we look at the last two equations, we see that the difference between selling 2 for $1 or 3 for $2 is $20, or:
We now have the total number of oranges and the price he got according to the original scheme. We can write
Putting these into the first equation, we get:
Answer : 80 of the first sort, 40 of the other.
Note : Not quite satisfactory, as he could not have sold the second sort by the 16's, but 4 for $3 would do.