Algebra Word Problem

Question

There are 100 plates seperated into 5 boxes. 

1st box + 2nd box = 52 plates

2nd box + 3rd box = 43 plates

3rd box + 4th box = 34 plates

4th box + 5th box = 30 plates

 

How many plates are in each box?

Answer 1

x, y, z, w, and v are plates 1, 2, 3, 4, and 5 respectively

x+y=52

y+z=43

z+w=34

w+v=30

x+y+z+w+v=100

(x+y)+z+(w+v)=100

52+z+30=100

z+82=100

z=18 plates

z+w=34

18+w=34

w=16 plates

w+v=30

16+v=30

v=14 plates

y+z=43

y+18=43

y=25 plates

x+y=52

x+25=52

x=27 plates

x=27 plates, y=25 plates, z=18 plates, w=16 plates, v=14 plates

27+25+18+16+14=100

Answer 2

 

Let x,y,z,v,w be the number of plates in boxes 1,2,3,4,5 respectively

 

 x+y = 52

 y+z  = 43

 z + v = 34

 v + w = 30

 

There is more than one (infinitely many) solutions to the system.

Letting w be the free variable:

  v = 30-w

  z = w + 4,

  y = 39 - w

 x = w + 13

 

So for example let there be w=10 plates in box #5

Then v = 30 - 10 = 20

z = 10 + 4 = 14

y = 39 - 10 = 29

x = 10 + 13  = 23

 

https://www.symbolab.com/solver/linear-system-of-equations-calculator

separates each each with a comma.