SOLUTION: An apartment renter must pay an initial $250 security deposit, and a monthly rent of $500. Write and graph an equation that gives the renter's average rent per month as a function

Question 1106386: An apartment renter must pay an initial $250 security deposit, and a monthly rent of $500. Write and graph an equation that gives the renter's average rent per month as a function of the number of months rented. After how many months will the average rent be $550?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you put down 250 security deposit.
the monthly rent is 500.

your total cost per month is the up front plus the monthly rent.

the formula would be y * x = 250 + 500 * x

y represents the average cost per month.
x represents the number of months.

to find out when the average cost per month will be 550, set y = 550 and solve for x.

you start with 550 * x = 250 + 500 * x

subtract 500 * x from both sides of the equation to get 50 * x = 250

divide both sides of the equation by 50 to get x = 5.

the average cost should be 550 per month in 5 months.

when x is equal to 5, the average cost per month equation becomes 5 * y = 250 + 5 * 500.

simplify this to get 5 * y = 2750.

divide that by 5 to get y = 550.

looks like the value of x is good.

you can graph the equation of y * x = 250 + 500 * x.

solve for y to get y = (250 + 500 * x) / x.

graph that equation and see what the value of x is when the value of y is 550.

the graph looks like this.

$$$

as you can see from the graph, the value of y is 550 when the value of x is 5.

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