Question 152834
Let's call the number of $8.50 paintbrushes, E.
Let's call the number of $9.75 paintbrushes, N.
"Paint Town sold 45 paintbrushes"
1.{{{E+N=45}}}
"In all, $398.75 was taken in for the brushes"
2.{{{8.50*E+9.75*N=398.75}}}
Use eq. 1 to solve for E as a function of N.
1.{{{E+N=45}}}
{{{E=45-N}}}
Now substitute that expression into eq. 2 and solve for N.
2.{{{8.50*E+9.75*N=398.75}}}
{{{8.50*(45-N)+9.75*N=398.75}}}
Let's multiply both sides by 100 to get rid of the decimal.
{{{850*(45-N)+975*N=39875}}}
{{{38250-850N+975N=39875}}}
{{{125N=1625}}}
{{{highlight(N=13)}}}
From above,
{{{E=45-N}}}
{{{E=45-13}}}
{{{highlight(E=32)}}}