ALgebra word problem
posted by mike .
a coffee shop sells a cup of espresso for $2.00 and a cup of cappuccino for 2.50. on friday, rachel sold 30 more cups of cappuccino than espresso, and she sold $178.50 worth of espresso and cappuccino together. how many cups of each were sold?

x espresso and y cappuccino
for x  2 x dollars
for y  2.5 y dollars
so
2x + 2.5 y = 178.5
but
y = 30 + x
so
2x + 2.5(30+x) = 178.5 
2e+2.5c=178.50 c=30+e
2e+2.5(30+e)=178.5
2e+75+2.5e=178.5
4.5e+75=178.5
4.5e=103.5
e=23,
c=30+e
c=30+23
c=53
Check it by plugging them back into the first equation; it works.