SOLUTION: a 30 lb bag of cement contains 35% cement and 65% sand. how much pure cement must be added to produce a cement mix that is 50% cement? i started to make a chart to help visualize,

Question 836249: a 30 lb bag of cement contains 35% cement and 65% sand. how much pure cement must be added to produce a cement mix that is 50% cement?
i started to make a chart to help visualize, but i don't know where to plug in any of the values
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Amount__|% as decimal|Total Pure
--------------------------------
__30____|__0.35______|_0.35(30)
__X_____|__1.00______|_1.00(X)
================================
_(30+X)__|__0.50______|_0.50(30+X)
(30+X) is the amount of product of the new mix
The total pure cement for our mix is
equal to 0.35(30) + 1.00(X).
The 0.35(30) is the amount of pure cement
in the original bag.
1.00 or 100% of the unknown X amount of cement
is represented by 1.00(X)
These two quantities together need to add
up the new 50% mix represented by 0.50(30+X)
So 0.35(30) + 1.00(X) = 0.50(30+X)
10.50 + X = 15 + 0.5X
add -0.5X to each side
10.50 + 0.5X = 15
add -10.50 to each side
0.5X = 4.50
X = 9
Our new mix is a total of 39 pounds.
The amount of pure cement in the new mix is 35% of 30 + 9 or
10.50 + 9 , 19.5 pounds of cement.
Since the new mix weighs 39 pounds, clearly 50% is cement.

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