Marcia bought a bag of marbles. there were twice as many purples ones as red ones there were 93 marbles in all. how many of each color marble were there?

R=number of red m arbles

p=number of purple marbles

2 times as many purple as red

p=2r

total is 93

r+p=93

we have

p=2r

r+p=93

subsitute 2r for p

r+2r=93

3r=93

divide 3

r=31

subsitute

p=2r

p=2 (31)

p=62

31 red

63 purble