1. ## story problem

Four boxes weigh 60 pounds all together, each box is twice as heavy as the next box. The lightest box is 20 pounds less than the 2 boxes in the middle combined. what are their weights?

2. Originally Posted by viet
Four boxes weigh 60 pounds all together, each box is twice as heavy as the next box. The lightest box is 20 pounds less than the 2 boxes in the middle combined. what are their weights?
Let the weights of the boxes be $\displaystyle a,b,c, \mbox { and }d$, with $\displaystyle a$ being the heaviest, $\displaystyle b$ the second heaviest and so on.

Then we have:

since the boxes weigh 60 pounds all together
$\displaystyle a + b + c + d = 60$ ......................(1)

since each box is twice as heavy as the next box
$\displaystyle a = 2b$ ...........................(2)
$\displaystyle b = 2c$ ...........................(3)
$\displaystyle c = 2d$ ...........................(4)

since the lightest box is 20 pounds less than the 2 boxes in the middle combined
$\displaystyle d = b + c - 20$ .....................(5)

so we have 5 equations and four unknowns, do you think we can find the unknowns?

3. im not sure, can we find it?

4. Originally Posted by viet
im not sure, can we find it?
haha, did you try?

(yes we can)

5. i understood how you setup the 5 equations. my mind is running a blank, so im pretty much lost on how to find the unknowns

6. Originally Posted by viet
i understood how you setup the 5 equations. my mind is running a blank, so im pretty much lost on how to find the unknowns
start by trying to write everything in terms of one variable, say a. try to change all the other letters so that they are expressions in terms of a. if you're still stuck after that, i'll walk you through it

7. Try and work from d, having d as the main variable as that is the lightest box.