Cost Accounting Problem?

Okay, I am working on a cost accounting problem for school and do not understand it. Can someone help me out a little? I don't need only an answer, please provide an explanation on how to solve. Thanks! Here is the problem:

The average cost per unit is $234 at a volume of 1,200 units and $205 per unit at a volume of 1,400 units. The profit was $24,000 at the lower volume. Estimate the variable cost per unit.

Some equations from the relevant chapter are:
Profit=Revenue-Costs.
Profit=(Price * Qty Sold) - (Variable Cost per unit * Qty sold) -Fixed Costs.

Revenue = (Fixed costs +profit)/(Price-variable costs)/price.

What do you think?

Yup, it's the Hi-Lo method alright. Here is how it goes:

$234 X 1,200 units = $280,800
$205 X 1,400 units = $287,000

The difference between the two costs above is $6,200.
We can safely assume that $6,200 represents changes purely in variable costs since we had an income $24,000 at the lower volume (it means fixed cost has been already covered).

Cost Movement $6,200.00
Units movement 200.00 units
Variable Cost per Unit $31.00

Therefore:

Variable Cost = $31
Fixed Cost = $243,600 (can be computed using the Variable cost)

I'm pretty sure you can use the high-low method to solve it. Look here : http://www.principlesofaccounting.com/ch...

Btw. I've got $31.

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