ASAP Aqua town charges $4.50 admission plus $0.75 for each ride. The cost at Wet World is $2.50 admission plus $1.25 per ride.

a) Write an equation for the cost of going to Aqua Town.

b) Write an equation for the cost of going to wet world.

c) How many rides would you have to ride for both water parks to cost the same amount? What would the cost be? Write a system of equations( put your two equations equal to each other)to solve for x and y. Write your answer in the form (x, y).

4 rides at each park will result cost $7.50.

Step-by-step explanation:

a) A(r) = 4.50 + 0.75r

b) W(r) = 2.50 + 1.25r

c) 4.50 + 0.75r = 2.50 + 1.25r

0.50r = 2

r = 4

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geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}