SOLUTION: To enter a very private garden you need to go through four doors. At each door you must pay an entry fee. If you pay $x at a given door, then you must pay $(2x + 1) at the next doo

Question 296197: To enter a very private garden you need to go through four doors. At each door you must pay an entry fee. If you pay $x at a given door, then you must pay $(2x + 1) at the next door. If it costs a total of $86 to get through the four doors, how much did you pay to get through the first door?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
To enter a very private garden you need to go through four doors. At each door you must pay an entry fee. If you pay $x at a given door, then you must pay $(2x + 1) at the next door. If it costs a total of $86 to get through the four doors, how much did you pay to get through the first door?
---------------
1st: x
2nd: 2x+1
3rd: 2(2x+1)+1 = 4x+3
4th: 2(4x+3)+1 = 8x+7
----------------------------
Solve: x + 2x+1 + 4x+3 + 8x+7 = 86
15x + 11 = 86
15x = 75
x = $5
=============
Cheers,
Stan H.
==============
RELATED QUESTIONS
essay show all work, a community 5k run will award $50 to the winner, 35 people enter the (answered by stanbon)

There are 4 shut doors in front of you. You know that each door has an animal painted on... (answered by richwmiller)

Is my answer correct? I would appreciate the feedback! A community 5K run will award... (answered by edjones)

Jerry signed up for a charity race in which he had to pay an entry fee of $35. BEfore the (answered by Tiffi0116,MathTherapy)

You are choosing between two plans at a discount warehouse. Plan A offers an annual... (answered by checkley77)

Your credit card has a balance of $6100 and an annual interest rate of 19%. You... (answered by Theo)

In a particular school there are exactly 1000 lockers numbered 1 to 1000. In this school (answered by rapaljer,richard1234)

Your Credit card has a balance of $5200 and an annual interest rate of 12%. You decide to (answered by Theo)

A recreational softball team paid a league entry fee of $825. The cost was covered by... (answered by stanbon,solver91311)