Question 569523
Let the two parts be x (the first part) and y (the second part).
x+y=24 and
7x+5y=146 makes your system of linear equations
We can combine them, subtracting 5 times the first equation from the second equation:
{{{7x+5y-5(x+y)=146-5*24}}} --> {{{2x=146-120=26}}} --> {{{highlight(x=13)}}}
Then we substitute the value found for x into the first equation to find y:
{{{13+y=24}}} --> {{{y=24-13}}}--> {{{highlight(y=11)}}}
Checking: {{{7*13+5*11=91+55=146}}}