SOLUTION: An artist makes $1,000 in profit after renting a booth and selling 50 prints. Another artist makes $550 after renting a booth and selling 32 prints. Which equation describes the r

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: An artist makes $1,000 in profit after renting a booth and selling 50 prints. Another artist makes $550 after renting a booth and selling 32 prints. Which equation describes the r      Log On


   

Question 1111731: An artist makes $1,000 in profit after renting a booth and selling 50 prints. Another artist makes $550 after renting a booth and selling 32 prints. Which equation describes the relationship between the number of prints sold, x, and the profit, y? F)y = -25x - 250 G)y = 25x + 250 H)y = 25x - 250 I)y = -25x - 250
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the equation will be:

y = 25x - 250

there's a built in assumption in this problem that the price of each print is the same for both artists.

you are given that:

1000 in profit is made after one artist sells 50 prints.

550 in profit is made after one other artist sells 32 prints.

the difference in profit is 1000 - 550 = 450.

the difference in the number of prints sold is 50 - 32 = 18.

amptjer built in assumption is that you are dealing with a straight line equation.

the slope intercept form of a straight line equation is y = mx + b.

m is the slope
b is the y-intercept.
y is the profit
x is the number of prints sold.

to find the slope, you take the change in the value of y and divide it by the corresponding chagnge in the value of x.

you would get m = 450 / 18 which simplifies to 25.

your equation becomes y = 25x + b

to solve for b, take any point that satisfies the equation and replace y with the y-value of that point and replace x with the x-value of that point.

i chose 50,1000 as my point.
32,550 would work just as well.

the equation of y = 25x + b becomes 1000 = 25 * 50 + b
simplify to get 1000 = 1250 + b
subtract 1250 from both sides and solve for b to get b = -250

the equation of y = 25x + b becomes y = 25x - 250.

the graph of this equation is shown below.

$$$

you can see that, when x is 0, the profit is -250.

this is the same as a loss of 250.

you can also eee that the artists will break even when 10 prints are sold at 25 dollars each.

you can also see that the artist that sells 32 prints makes 550 in profit.

you can also see that the artist that sells 50 prints makes 1000 in profit.

i believe your selection is H.