Dante's Infernal Puzzle Collection -- 16. Frutta

We will use the following notation:
A: weight of one apple
L: weight of one plum
P: weight of one peach

According to the information given to us, we know:
1) 3A + 1P = 10L
2) 1P = 6L + 1A

And we need to solve for x in the following equation.
1P = xL

Recall that 1P = 6L + 1A. so xL = 6L + 1A.
From equation 1) above, 3A + xL = 10L, and thus 3A = (10-x)L, which means 1A = [(10-x)/3]L.
Plugging this back into the above equation (xL = 6L + 1A), we get xL = 6L + [(10-x)/3]L.
Multiply both sides by 3 --> 3xL = 18L + 10L - xL.
Collect terms --> 4xL = 28L
x = 7.

Answer: 7 plums.