Quantitative Analysis in budgeting

The management accountant of a business has identified the following information;

Activity level 800 units 1200 units

Total costs $16,400 $23,600

The fixed costs of the business step up by 40% at 900 units
What is the variable cost per unit.

The kit calculated $8

This is not because i did not understand the process but if there is any other short way in case it is objective questions.

Using the liner model, TC= FC + VC

23,600 = 1.4FC + 1200 VC AND 16,400 = FC + 800VC

23,600- 1200VC = 1.4FC 16.400 – 800VC = FC

23,600 -1200vc/ 1.4 = FC

Using Substitution ,
16400 – 800vc = 23600- 1200vc/1.4
22960- 1120vc= 23,600 – 1200vc
23,600- 22960= 1200-1120
640= 80vc
vc = 640/80 = $8.

Please, assist if there is any shorter way to calculate this.

Thanks.