multi step equation

Question

Nancy has a freshwater aquarium at home. She buys goldfish four more than twice the number of platies she bought last Sunday. She also buys 2 black mollies and a few guppies that amounted to one quarter of the total number of goldfish she bought. If there are 35 fish in all, how many goldfish did she buy?

Answer 1

let gold = number of goldfish

let p = number of platies

let gup = number of guppies

second sentence tells us

gold = 4 + 2p

third sentence tell us

gup = 1/4 of gold = 0.25•gold

last sentence indicates

35 = gold + p + gup + 2

substituting the other info, we can get

35 = (4 + 2p) + p + [0.25•(4 + 2p)] + 2

= 4 + 2p + 1p + 1 + 0.5p + 2

35 = 7 + 3.5p subtract 7 from both sides

28 = 3.5p divide both sides by 3.5

8 = p

since gold = 4 + 2p, then gold = 4 + 2(8) = 4 + 16 = 20

20 gold fish

(incidentally, gup = 0.25(20) = 5

we found p = 8

there are 2 black mollies

that adds up to 35 fish