SOLUTION: A certain concrete mixture contains 5% cement and 8% sand. How many pounds of this mixture and how many pounds of sand should be combined with 255 pounds of cement to make a batch
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Question 892804: A certain concrete mixture contains 5% cement and 8% sand. How many pounds of this mixture and how many pounds of sand should be combined with 255 pounds of cement to make a batch that is 12% cement and 15% sand? Set-up is my issue Found 2 solutions by josmiceli, josgarithmetic:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Let = pounds of the 5% cement
and 8% sand mixture needed
--------------------------- = pounds of cement in this mixture = pounds of sand in this mixture
---------------------------
Let = pounds of additional sand to be added
Also pounds of cement are added
---------------------------------------
(1) Total pounds of mixture =
----------------
The pounds of cement in final mixture:
(2)
--------------------------------------
The pounds of sand in final mixture:
(3)
--------------------------------------
This is 2 equations and 2 unknowns, so it
should be solvable. If you don't mind, I'll try to solve it
so I can check it
----------------------------------
(2)
(2)
(2)
(2)
---------------------------
(3)
(3)
(3)
-------------------------
Add (2) and (3)
(3)
(2)
------------------------
and
(2)
(2)
(2)
(2)
---------------------
--------------------
------------------
137.08 pounds of cement from the mixture
219.32 pounds of sand from the mixture
270.77 pounds of additional sand
are needed to make 12% cement and 15% sand mixture
--------------------------------
check:
(2)
(2)
(2)
(2)
That's hopeful- you can check the other equation
if you agree with my basic setup that is.
Hope this helps
You can put this solution on YOUR website! 255 pounds of cement;
x pounds of the available mixture;
s pounds of sand;
Resulting Mix must be 12% cement and 15% sand.
You not yet know exactly the quantity of the resulting mix, but you know it will be 255+x+s pounds.
Account for Cement Result:
Account for Sand Result:
Each of those accounting equations is written for decimal fractions instead of using percents. The equations appear as rational form but working through them to simplify shows each is a linear equation in x and s.
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