SOLUTION: You purchase 8 gal of paint and 3 brushes for $152.50. The next day, you purchase 6 gal of paint and 2 brushes for $113.00. How much does each gallon of paint and each brush cost?

Algebra ->  Systems-of-equations -> SOLUTION: You purchase 8 gal of paint and 3 brushes for $152.50. The next day, you purchase 6 gal of paint and 2 brushes for $113.00. How much does each gallon of paint and each brush cost?      Log On


   



Question 816587: You purchase 8 gal of paint and 3 brushes for $152.50. The next day, you purchase 6 gal of paint and 2 brushes for $113.00. How much does each gallon of paint and each brush cost?
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
x = cost per gallon of paint and y = cost per brush
Day 1 : 8x+%2B+3y+=+152.50
Day 2 : 6x+%2B+2y+=+113.00


We are going to solve day 2 for y so we can plug y into day 1.
6x+%2B+2y+=+113.00
2y+=+-6x+%2B+113.00
y+=+-3x+%2B+56.50
Now since we know what y equals, we can use the substitution method and plug y into the day 1 equation.


8x+%2B+3%28-3x+%2B+56.50%29+=+152.50
8x+-+9x+%2B+169.50+=+152.50
-x+%2B+169.50+=+152.50
-x+=+-17
x+=+17
the cost of a gallon of paint is $17. plug 17 in for x in the day 1 equation to find y.


8%2817%29+%2B+3y+=+152.50
136+%2B+3y+=+152.50
3y+=+16.50
y+=+5.50
The cost of a single brush is $5.50.