3. A manufacturer makes a profit of $1,500 when 45 items are sold, and a profit

Question

3. A manufacturer makes a profit of $1,500 when 45 items are sold, and a profit of $2,500 when 65 items are sold. a) Write a linear equation, in slope-intercept form, which describes the relationship between the profit, y, and the number of items sold, x. b) Use the equation to find the expected profit if 100 items are sold? Show how you get your answer. e) Use the equation to find how many items need to be sold if the profit is to be $5000? Show how you get your answer. 4. Determine the domain of each relation, and determine whether each relation describes y as a function of x. For any which are not functions, explain why. a) y = 5x-10 c) y = 2x-4 5. Rewrite each of the following with positive exponents only and in simplified form. Do NOT use any decimals. b) -62 e) (- 6)2 e) () 2

Explanation / Answer

3) ( 45 , 1500) and ( 65 , 2500 )

slope = ( 2500 - 1500 ) / (65 - 45)

slope m = 50

applying point slope form

y - 1500 = 50 ( x- 45 )

y = 50x - 750

a) linear equation is y = 50x - 750

b) if 100 items were sold

expected profit is y = 50(100) - 750

= $ 4250

c) 5000 = 50x -750

5750 / 50 = x

x = 115

so, 115 items needed to be sold to make a profit of $ 5000

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