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?