SOLUTION: Hi, I would just like to say thank you in advanced for your help. My question is as follows: A certain mixture contains 5% cement and 8% sand. How many kilograms of this mi

Question 1002836: Hi,
I would just like to say thank you in advanced for your help. My question is as follows:
A certain mixture contains 5% cement and 8% sand. How many kilograms of this mixture and how many kilograms of sand should be combine with 255 kilograms of cement to make a batch that is 12% cement and 15% sand?
Thank you again
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Current mixture, 5% cement and 8% sand
Want to combine quantities m of current mixture, x of sand, 255 kilograms of current mixture;
Result to be 12% cement and 15% sand

Mass in kilograms of the result mixture, m+x+255

The accounting equations are setup here using decimal fractions instead of percentage units.

Accounting sand

Accounting cement

The starting system of equations in m and x is
.
Can you solve this system, and do you find meaningful results for m and x ?

Carefully simplifying the system of equations gives the equivalent system

The use of substitution method might be the preferable way to solve this system.

If the analysis is correct, and the solution steps are done correctly, and if either found value
is nonsense, or negative, then this means the description was bad, and the problem has no solution.

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