The graph of p = 400 and the graph of p = 50s - 200 intersect at the point (12,400). If the equation p = 50s - 200 represents the profit, p, based on s sales, what does the intersection best represent? Show work.

This shows that the profit for 12 sales is 400

Step-by-step explanation:

If both graphs intersects then;

p = p

400 = 50s - 200

50s = 400+200

50s = 600

s = 600/50

s = 12

Substitute s =12 into p = 50s-200

p = 50(12) - 200

p = 600-200

p = 400

Hence the intersection (s, p) is (12, 400)

This shows that the profit for 12 sales is 400

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 .