Help with Algebra please!

Here is the question, For a school fundraiser, jay sold 12 boxes of stationery and 8 boxes of envelopes for a total of $41.00. sue sold 18 boxes of stationery and 16 boxes of envelopes for $68.50. How much did one box of envelopes cost? Can anyone help and explain this please? I have no clue how to do this cuz my teacher didnt show us how.

let consider cost of one box of stationery be x and one box of envelope be y.
Then, from question, we can have an equation,

12x + 8y =$41.00..............................(i)
18x + 16y =$68.50.............................(ii)

Multiply equation (i) by 3 and multiply equation (ii) by 2. Then subtract (ii) form (i). You will have,

8y = $14.00
y = $1.75.

So cost for one box of envelope is $1.75

ok well first, you have to find out what 's' is (stationary box cost) so this wud make a simulateous equation.

s= stationary boxes e= envelope boxes

1) 12s + 8e= 41 (equation 1)
18s + 16e= 68.5 (equation 2)

2) Multiply equation 1 by 8 and equation 2 by 16 so they both have the same number

12s + 128e= 41
18s + 128e= 68.5

3) Move the unknowns onto the other side of the equation by taking them away

128e = 41 - 12s
128e = 68.5 - 18s

4) since both equations equal 128e, it makes sense to write it out like this:

41 - 12s = 68.5 - 18s

5) now take away the smaller unknown (-12) from the bigger unknown (-18) by adding +12 to both unknowns to get rid of it: (+12 - 12= 0) (+12 -18 = -6)

41= 68.5 - 6s

6) Now take away 68.5 on both sides (41 - 68.5 and 68.5 - 68.5)

-27.5= -6s or -6s= -27.5

7) Now divide -27.5 by -6

s= $4.50
to find out 'e', substitute 's' in the previous equation with 4.5


12(X 4.5) + 8e= 41
18(X4.5) + 16e= 68.5

54+ 8e=41
81+16e= 68.5

Minus 41 and 68.5 on both sides

13 + 8e= 0
12.5 + 16e = 0

move 8 and 16 onto the other side..

13= -8e
12.5= -16e

now divide 13 by 8...

$1.75= e

Long but helps in ALL simultaneous equations!

Hope this helped x

Set up an equation.
x-Stationary.
y-Envelopes.

12x + 8y = $41.00.
18x+ 16y=$68.50.

The mulitply your first equation by -2.

So you get -24x - 16y=-$48.00.
then you cancel it out,
so you get -6x=$20.50

Lol yeah idk if i'm right or not. but i'm pretty sure.

12S + 8E = 41 times 2 makes 24S + 16E = 82
18S +16E = 68.5 subtract equations
6S = 13.5
S = $2.25 now substitute
E = $1.75

thats what Internet is for