equations and inequa;ities

Question

Marie is cleaning her clothes out of the closet in her spare bedroom. She started with 650 of her items in the closet. She has been able to continually decrease the number of her items in the closet at a rate of one-half per month. Her brother, Dustin, has started putting 5 items of his clothing in the closet each month as Marie cleans it out. Marie wants to know how many months it will take before the number of items Dustin adds will be equal to the number of her items in the closet.

Create a system of equations to model the situation above, and use it to determine if there are any solutions. If there are any solutions, determine if they are viable or not.

Answer 1

f(t) = 650(2)^-t

g(t) = 5t

If you plot both equations, there is an intersection at t = 4.768, f(t) = 23.8

When t = 4 months, Marie has 40 and Dustin has 20

When t = 5 months, Marie has 20 and Dustin has 25

So in between 4 and 5 months they will both have 24 pieces of clothing.

If they only subtract and add once a month, they will never have the same number of clothes at the same time.