Question 175877
This is a three equation process and we work our way from one to the next:

First we need to translate the word problem to a number problem:
Let k=price of skunk pelts
Let q=Price of squirrel pelts
Let r=Price or raccon pelts
4 skunk pelts, 6 squirrel pelts, and 8 raccoon pelts, and he charged them $572.
4k+6q+8r=572

The second was for 10 squirrel pelts and 10 raccoon pelts, for which he charged $370. 
10q+10r=370

The third order was for 45 squirrel pelts, and he charged $540 for that order
45q=540


From this last equation we divide all terms by 45 and get:

{{{45q/45=540/45}}}
{{{q=12}}}

Now we replace q by 12 on the second equation:
{{{10q+10r=370}}}
{{{10(12)+10r=370}}}
{{{120+10r=370}}}
{{{10r=370-120}}}
{{{10r=250}}}
{{{r=250/10}}}
{{{r=25}}}
Last step is to replace r and q on the first equation
{{{4k+6q+8r=572}}}
{{{4k+6(12)+8(25)=572}}}
{{{4k+72+200=572}}}
{{{4k=572-72-200}}}
{{{4k=572-272}}}
{{{4k=300}}}
{{{k=284/4}}}
{{{k=75}}}

Skunks= $75
Raccoons= $25
Squirrels= $12

We can replace numbers on all three equations to verify.