Agoldfish cost $12. an angelfish costs 75% less. sam paid $198 for some goldfish and angelfish. 60% of the fish he bought were angelfish. how much more money did he spend on goldfish than angelfish?

Price of goldfish = $12
Price of angelfish = 0.75*12 = $3

If the number of goldfish is x and the number of angelfish is y then:
198 = 12x + 3y
x + y = z (with z being the total number of fish bought)

Now if we use the information that 60% of the fish bought were angelfish we can say:
198 = 12*0.4z + 3*0.6z
198 = 4.8z + 1.8z
198 = 6.6z
z = 30

So if he bought 30 fish in total and 60% of them were angelfish then the number of angelfish is:
30*0.6 = 18

If the price of each angelfish is $3, then he payed:
18*3 = $54

If the price of each goldfish is $12, then he payed:
12*12 = $144

Now we can subtract the cost of the angelfish from the cost of the goldfish:
144 - 54 = $90

Therefor he spent $90 more on goldfish than angelfish

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.