Johnson had 1/3 as many red marbles as blue marbles. If he bought another 12 red marbles, he would have 2/5 as many red marbles. How many marbles did Johnson have altogether?

Answer 1

blue marbles ---- x
red marbles ----- (1/3)x = x/3

if ....
x/3 + 12 = (2/5)x
times 15
5x + 180 = 6x
x = 180

number of blue is 180, number of red is 60 for a total of 240

check:
at start: blue = 180, red = 60 , red is 1/3 of blue
after buy: blue = 180, red = 72, and 72/180 = 2/5
all is good !