For $360, a rock-climbing gym offers yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. write an equation to find the number of visits after which the total cost for a member and the total cost for a nonmember are the same. then solve the equation.

So, we have the two equations $4x+$360, and $10x+$6x. x represents how much members pay each day. The total number of visits when the cost for a member and nonmember is the same means we will have to set both equations equal to one another. 
$4x+$360=$10x+$6x 
Combine like terms. 
$4x+$360=$16x 
Subtract $4x on both sides to balance out the equation. 
$12x=$360 
Divide by $12.00 on each side. 
x=30 visits 
To check your work, plug in what x equals or 30 in the original equation. If you come up with a true statement, then you know your answer has to be correct. 
4x+360=16x 
4(30)+360=16(30) 
120+360=480 
480=480 
Because this is a true statement, you can be certain that the total number of visits when the cost of a member and a nonmember will be the same is 30 visits. Hope I helped! Brainliest too please.