Question 573671
Mr. Green and Mr. Martin played a game of marbles.
 At first, the ratio of MR.Green;s to Mr. MArtins marbles was 8:3.
 But then Mr.Green gave 45 of his marbles to Mr. Martin.
 In the end they both had the same amount of marbles. 
How many marbles did Mr.Green start with?
:
Let g = Green's marbles originally
Let m = Martin's original number
:
{{{g/m}}} = {{{8/3}}}
Cross multiply
8m = 3g
m = {{{3/8}}}g
:
g gave 45 to m
g - 45 = m + 45 
g = m + 45 + 45
g = m + 90
Replace m with {{{3/8}}}g
g = {{{3/8}}}g + 90
g - {{{3/8}}}g = 90
{{{5/8}}}g = 90
multiply both sides by 8
5g = 8(90)
5g = 720
g = 720/5
g = 144 marble, Mr Green started with
:
:
You can check this by finding m and putting it in the 1st equation