Question 1184096
The ratio of Devi’s marbles to Eddie’s marbles was 2:5.
 After Devi gave away 8 marbles and Eddie gave away 40 marbles, the ratio of
Devi’s marbles to Eddie marbles became 1:2.
How many marbles did Devi have at first?
:
let x = the multiplier
then
2x = D's marbles originally
and
5x = E's marbles originally
:
"After Devi gave away 8 marbles and Eddie gave away 40 marbles, the ratio of
Devi’s marbles to Eddie marbles became 1:2. "
{{{(2x-8)/(5x-40)}}} = {{{(1x)/(2x)}}}
cancel the second fraction's x's
{{{(2x-8)/(5x-40)}}} = {{{1/2}}}
cross multiply
5x - 40 = 2(2x-8)
5x - 40 = 4x - 16
5x - 4x = -16 + 40
x = 24 is the multiplier
therefore
2*24 = 48 marbles D had originally
:
Check solution with substitution in the first equation
{{{(48-8)/(120-40)}}} = {{{(40)/(80)}}}