Simultaneous equations help

A barbecue manufacturer makes 2 models, the Outback and Bush Walker. It is known that 20 percent more of the Outback model is sold than the Bush Walker. A profit of $200 is made on each Outback sold but $350 is made on each Bush Walker. If during the next year a profit of $177000 is planned, how many of each barbecue must be sold?

How would I go about doing this? I've already tried but I can't seem to get a start. Can someone start me off?

All I have atm is

Let a be the total number of Outbacks sold and b is Bushwalkers sold

$\displaystyle 200a+350b = 177000 $

Well I figured some more out. Since there is 20 percent more of $\displaystyle a$ sold than $\displaystyle b$ that means $\displaystyle b=0.8a$

If I sub that in I get a=368.75 and b=295

Is this right?