need help with math problem for my son?

Question

you purchase 8 gallons of paint and 3 brushes for $152.50. the next day, you purchased 6 gallons of paint and 2 brushes for $113.00. how much dose each gallon of paint and each brush cost?

Answer 1

Let g=price of gallon of paint and b=price of brush.
Then we can write 8*g+3*b=152.50 and 6*g+2*b=113.00.
Multiply the first by 2: 16*g+6*b=305.
Multiply the second by 3: 18*g+6*b=339.
Subtract the first from the second to get 2*g=34. Divide by 2 to get g=17 (A gallon costs $17)
Plug this value into the very first equation and solve for b.
3b=152.50-8*17=16.5
Divide by 3. b= 5.5 (A brush costs $5.50)
Check: 8*17+3*5.5=152.50, 6*17+2*5.5=113.

Answer 2

8P+3B = 152.50 (equation 1)
6p+2B = 113 (equation 2)

Multiply Eq.1 by 2 and Eq. 2 by 3 will give
16P + 6B=305 (eq 3)
18p + 6B = 339 (eq 4)

Subtract eq-3 from eq-4 (that is, eq4 - eq3) will give

2P= 34Therefore, P = 17

Now, plug P = 17in any of the four equations (let us plug in eq-1)

8(17) + 3B = 152.50
that is , 136+ 3B = 152.50
therefore, 3B = 152.50- 136 = 16.50
Hence, B = 5.50


So, each gallon of paint is $17 and each brush is $5.50

Answer 3

No it's not for me, its for , uhh ... my son! Yes, this is a question for my son! I'm not cheeting on my homework!

The answer is easy if you've ever painted a house.
8p + 3b = 152.50
6p + 2b = 113.00

so reformat the second equation
b = (113 - 6p)/2
and substitute into first equation
8p + 3(113 - 6p)/2 = 152
which is then
8p + 169.5 - 9p = 152
then
-1p = -17.5
and
p = 17.5 (dollars per gallon of paint)
substitute that back into one of the first equations, like the reformated one
b = (113 - 6 * 17.5)/2
and then
b = 4 (dollars per brushe)

Yes. My answer is wrong. But you get the point. His third grade teacher will be impressed with the algebra your son knows. Let me know where I can buy these items where tax isn't included.

Answer 4

okay:

8x + 3y = 152.50, and
6x + 2y = 113.00 solve one for one variable, in this case:

6x = 113.00 - 2y
x = (113.00 - 2y)/6

Substitute into the first equation:

8[(113 - 2y)/6] + 3y = 152.50

Simplify:

452 - 8y = 457.50 - 9y, or
y = 5.50.

Put that back to the original equation of

x = (113 - 2y)/6 or x = [113 - 2(5.50)]/6

and solve for x = 17

Gallon of paint (x) = $17.00
Brush (y) = $5.50

Answer 5

8p + 3b = 152.50

6p + 2b = 113

(solve for one of the variables)

6p = 113-2b
p = (113-2b)/6

plug that into the 1st equation:

8[(113-2b)/6] + 3b = 152.50

multiply everything by 6 to get rid of the denominator:

8(113-2b) + 18b = 915
904 - 16b + 18b = 915
2b = 11
b = $5.50

so, p = (113-2*5.50)/6 = $17

check:

8 ($17) + 3(5.50) = 152.50
136 + 16.5 = 152.50

check! :)

Answer 6

1 gallon is $17 and 1 brush is $5.50

Answer 7

a) 8x + 3y =152.50
b) 6x + 2y = 113.00

solving equation b for y
y = (113 - 6x)/2 = 56.50 - 3x

substituting this value for y into equation a
8x + 3(56.50 -3x) = 152.50

solve for x
x = 17
y = 5.50

paint is $17/gallon
brushes are $5.50

Answer 8

paint= $17
brush= $5.50

explanation:
x=paint y= brush

2 equations- 1) 8x+3y= 152.5
2) 6x+2y= 113

make one equation to = y or x. i just picked the 2nd equation:
x= (113-2y)/6

substitute that into the first equation and solve for y.
plug that y value in to solve for x.

Answer 9

use x and y and solve one equation for X then subsitiute the x's in the first for the solved equation. Then work the equation to find y.

Answer 10

g=gallons
b=brushes

8g+3b=152.50
6g+2b=113
----------------
2b= (-6g)+113
b= (-3g)+56.5

8g+3(-3g+56.5)=152.5
8g-9g+169.5=152.5
-1g= (-17)
g=17

6(17)+2b=113
102+2b=113
2b=11
b=5.5

each gallon costs $17.00 and each brush costs $5.50