SOLUTION: Mike is loading four boxes of provisions on his boat. Together the boxes wigh 80 lbs. Each box is 1/3 the weight of the next heavier box. What is the weight of each box? That

Question 233219: Mike is loading four boxes of provisions on his boat. Together the boxes wigh 80 lbs. Each box is 1/3 the weight of the next heavier box. What is the weight of each box?
That is the problem I'm trying to solve. Ok well I've solved it, but i need to know how you would "show" how to solve it. I'm a Guess/Checker and came up with
2;6;18;54 for the 4 boxes. How would i go about solving that mathematically though? It's for my Wife's Elementary Math class, and she has to do a bit more than my guess and check method.
Thanks!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let the boxes be a, b, c, d

a = b/3
b = c/3
c = d/3

this means that:

d = 3*c
d = 3*b
b = 3*a
a = a

you have a + b + c + d = 80

replace d with 3*c to get:

a + b + c + 3*c = 80

replace c with 3*b to get:

a + b + 3*b + 3*3*b = 80

replace b with 3*a to get:

a + 3*a + 3*3*a + 3*3*3*a = 80

simplify and combine like terms to get:

a + 3*a + 9*a + 27*a = 80 which becomes:

40*a = 80 which becomes:

a = 2

you get:

a = 2
b = 3*2 = 6
c = 3*3*2 = 18
d = 3*3*3*2 = 54

your answers are:

a = 2
b = 6
c = 18
d = 54

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