Question 1002836
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
{{{(0.08m+x+0*255)/(m+x+255)=0.15}}}


{{{(0.08m+x)/(m+x+255)=0.15}}}


Accounting cement
{{{(0.05m+0*x+255)/(m+x+255)=0.12}}}


{{{(0.05m+255)/(m+x+255)=0.12}}}


The starting system of equations in m and x is
{{{system((0.08m+x)/(m+x+255)=0.15,(0.05m+255)/(m+x+255)=0.12)}}}.
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
{{{system(0.85x-0.07m=38.25,0.12x-0.38m=224.4)}}}


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.