SOLUTION: 1)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 ->  Coordinate Systems and Linear Equations -> SOLUTION: 1)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 954947: 1)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?
2)Shopping at Savers Mart,Lisa buys her children four shirts and three pairs of pants for $85.50. She returns the next day and buys three shirts and five pairs of pants for $115.00. What is the price of each shirt and each pair of pants ?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
PROBLEM 1)
G=gallon of paint; B=brush
8G+3B=$152.50 Multiply Each side by 2.
16G+6B=$305.00 Use this to subtract below.
6G+2B=$113 Multiply each side by 3.
18G+6B=$339.00 Subtract equation from above.
16G+6B=$305.00
2G=$34
G=$17 ANSWER 1: a gallon of paint costs $17.
8G+3B=$152.50 Use value for G.
8($17)+3B=$152.50
$136+3B=$152.50 Subtract $136 from each side.
3B=$16.50 Divide each side by 3.
B=$5.50 ANSWER 2: Each brush cost $5.50.
CHECK:
6G+2B=$113
6($17)+2($5.50)=$113
$102+$11=$113
$113=$113
.
PROBLEM 2)
S=shirt; P=pants
4S+3P=$85.50 Multiply each side by 3.
12S+9P=$256.50 Use this to subtract below.
3S+5P=$115.00 Multiply each side by 4
12S+20P=$460 Subtract equation from above.
12S+9P=$256.50
11P=$203.50 Divide each side by 11.
P=$18.50 ANSWER 1: Pants cost $18.50.
4S+3P.=$85.50 Use value of P
4S+3($18.50)=$85.50
4S+$55.50=$85.50 Subtract $55.50 from each side.
4S=$30 Divide each side by 4.
S=$7.50 ANSWER 2: Shirts cost $7.50.
CHECK:
3S+5P=$115.00
3($7.50)+5(18.50)=$115
$22.50+$92.50=$115
$115=$115