First, we know that he spent $4.80 (5-20c), we know the total mass of the potatoes he bought, and we know the price of each type of potato.
We are dealing with 2 equations here:
o+n=18 (for "old plus new equals 18")
0.22o + 0.36n = 4.80 (for the prices of the old and new potatoes).
What you need to do now is combine the equations. I did this by multiplying the first equation by 0.22:
o + n = 18
(you have to multiply 0.22 to both sides of the equation, including 18)
What you end up with is this new equation:
0.22o + 0.22n = 3.96
You then subtract this equation from the other equation like this:
0.22o + 0.36n = 4.80
- (0.22o + 0.22n = 3.96)
0 + 0.14n = 0.84
So we can see that we have completely cancelled out o, leaving us with only n to deal with.
Now our new equation is:
0.14n = 0.84
solving for n, we get
n = 6
and that is the mass of the new potatoes he buys.