Question 162434
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1st condition:
{{{12kPT+6kRC=732}}} ----------------------> EQN 1
{{{9kPT+13kRC=923}}} ----------------------> EQN 2
In EQN 1 we get,
{{{RC=(732-12kPT)/6k}}} -------------------> EQN 3
Subst. EQN 3 in EQN 2:
{{{9kPT+13k((732-12kPT)/6k)=P923}}}, Distribute
{{{9kPT+((9516-156kPT)/6)=P923}}}, Add by getting common denominator "6"
{{{(54kPT+9516-156kPT)/6=P923}}}, cross multiply
{{{54kPT+9516-156kPT=923*6=P5538}}}
{{{P9516-P5538=156kPT-54kPT}}}, Combine similar terms
{{{P3978=102PT}}}
{{{cross(P3978)P39/cross(102)=cross(102)PT/cross(102)}}}
{{{PT=P39.00/k}}}, cost of Potato per kilo
Go back EQN 3:
{{{RC=(732-12*39)/6=(732-468)/6=264/6}}}
{{{RC=P44.00/k}}}, cost of Rice per kilo
In doubt? Go back EQN 1 
{{{12*39+6*44=732}}}
{{{468+264=732}}}
{{{P732.00=P732.00}}}
Via EQN 2:
{{{9*39+13*44=923}}}
{{{351+572=923}}}
{{{P923.00=P923.00}}}
Thank you,
Jojo</pre>