Question

ASAP

Hermes has eight envelopes labeled "x" and an additional $218, and Apollo has five envelopes labeled "x" and an additional $521.Each envelope has the same amount of money in it.

a) Write a system of equations representing this situation

b) How much money must be in each envelope for them to have the same amount of money?​​​

Answer 1

a)
`\left \{ {{8x+218=y} \atop {5x+521=y}} \right.`, b) $101

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.

`\left \{ {{8x + 218 = H} \atop {5x +521 = A}} \right.`

If Apollo and Hermes both had the same amount of total money, A and H could equal y

`\left \{ {{8x+218=y} \atop {5x+521=y}} \right.`

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:

`8x+218=5x+521`

Subtract
`5x` from both sides

`3x+218=521`

Subtract 218 from both sides

`3x=303`

Divide both sides by 3

`x=101`

So there would have to be $101 in both envelopes for Apollo and Hermes to have the same amount of total money.