Questions on Algebra: Systems of Linear Equations answered by real tutors!

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Question 152834: Paint Town sold 45 paintbrushes, one kind at $8.50 each and another at $9.75 each. In all, $398.75 was taken in for the brushes. How many of each kind were sold?
: Paint Town sold 45 paintbrushes, one kind at $8.50 each and another at $9.75 each. In all, $398.75 was taken in for the brushes. How many of each kind were sold?

Answer by Fombitz(1755) About Me  (Show Source):
You can put this solution on YOUR website!
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)