Answer:
a) [tex]\left \{ {{8x+218=y} \atop {5x+521=y}} \right.[/tex], b) $101
Step-by-step explanation:
Hermes: 8 envelopes, $218
Apollo: 5 envelopes, $521
If x is the amount in each envelope, H is the amount Hemes has and A is the amount Apollo has, this would be a possible system of equations.
[tex]\left \{ {{8x + 218 = H} \atop {5x +521 = A}} \right.[/tex]
If Apollo and Hermes both had the same amount of total money, A and H could equal y
[tex]\left \{ {{8x+218=y} \atop {5x+521=y}} \right.[/tex]
We want to find the amount in each envelope (x), so we can substitute y in the first equation for y in the second equation:
[tex]8x+218=5x+521[/tex]
Subtract [tex]5x[/tex] from both sides
[tex]3x+218=521[/tex]
Subtract 218 from both sides
[tex]3x=303[/tex]
Divide both sides by 3
[tex]x=101[/tex]
So there would have to be $101 in both envelopes for Apollo and Hermes to have the same amount of total money.
