A sporting goods store added 50% profit cost and 8% tax to the price of a backpack, which
then became $129.60. What was the price of
the backpack before adding profit and tax?

p q⋅ = ×− =− 32 6 .

Explanation:

A

y mx b = + Slope-Intercept Form

1

3 y xb = +

1

3 m =

1 1 (6) 3

−= + b (6, 1) − is on the graph.

− = 3 b

Thus equation of the line that has slope 1

3

and

contains the point (6, 1) − is 1 3

3 y x = − .

The slope of the second line is 0 1

1 0

−

− , or −1 .

The equation of the second line is

y x − =− − 1 1( 0) , or y x =− +1.

Substitute − +x 1 for y in the equation

1 3

3 y x = − .

1 1 3

3

−+= − x x ⇒

4 1 3

3 = −x ⇒

4 4

3 = x

⇒ 3 = x

Substitute 3 for x in the equation y x =− +1,

to solve for y . So, y =− + =− (3) 1 2 .

The point of intersection is (3, 2) − .

Therefore, p = 3 and q = −2, so

p q⋅ = ×− =− 32 6 .

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