SOLUTION: How many items are in each box if 900 Items are divided among three boxes such as the first box contains half of the second box while the third box contains thrice of the first box

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Question 1034492: How many items are in each box if 900 Items are divided among three boxes such as the first box contains half of the second box while the third box contains thrice of the first box?
All I know is the first box =150
The second box is = 300 and the third box is = 450
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
a = the number of items in the first box.
b = the number of items in the second box.
c = the number of items in the third box.

you get a + b + c = 900

you are given that a = b/2 and you are given that c = 3a.

since a = b/2, you can determine that b = 2a.

you now know that:

a = a
b = 2a
c = 3a

replace b and c in the equation of a + b + c = 900 to get a + 2a + 3a = 900.
combine like terms to get 6a = 900
solve for a to get a = 150.
since b = 2a, then b = 300.
since c = 3a, then c = 450.

problem is solved.
first box contains 150 items.
second box contains 300 items.
third box contains 450 items.