Math riddle

if a man takes 7 dollars from a second man, he will then have five times the dollars of the second man.

if the second man takes 5 dollars from the first man, he will then have seven times the dollars of the first man. how much money does each have?

X=man 1
y=man 2

x+7 and y-7
then
(x+7)=5(y-7)

y+5 and x-5
(y+5)=7(x-5)

so equations are
x+7=5(y-7)
and
y+5=7(x-5)
distribute

x+7=5y-35
y+5=7x-35

subsitution
minus 5 both sides for 2nd equation
y=7x-40
sub 7x-40 for y in other equation

x+7=5(7x-40)-35
expand
x+7=35x-200-35
x+7=35x-235
minus 7 both sides
x=35x-242
minus 35x both sides
-34x=-242
divide both sides by -34
x=7.11765
first guy has about 7.12

sub back

y=7x-40
y=7*(7.11765)-40
y=9.82353
round
9.82

first guy has $7.12
2nd has $9.82

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