) Write a system of equations to describe the situation below, solve using substitution, and
fill in the blanks.
)) A business owner wants to have the front window of his store painted and is considering
two artists for the job. Bryce has quoted a flat rate of $250 for the job. Heather's quote is
$43 per hour, plus $78 to cover the cost of materials. Depending on how long it takes
Heather to paint the window, these two could end up charging the same amount. How much
would it cost? How long would Heather have to take?
)) The cost would be $1
with either artist if the job took Heather
hours.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

final total: 63

step-by-step explanation:

60 times sales tax

60 times 0.05

3

60 + 3

63