Question 296654
You're using "1" instead of "l" but I think you mean lattes, right?
I'll just capitalize. 
Your setup is correct. 
{{{L + C = 30}}}
{{{4L +3C =100}}}
.
.
.
{{{4(30-C)+3C=100}}}
{{{120-4C+3C=100}}}
{{{-C=-20}}}
{{{C=20}}}
Then
{{{L=30-C=30-20=10}}}
Your answer is correct also. 
He can buy 20 cappucinos and 10 lattes if he wants to exactly use $100 and buy exactly 30 drinks. He could also buy 30 cappucinos and have $10 left over.