Question

A carnival has two payment options. Plan A, you pay $10 admission plus $3 for each ride. Plan B, you pay a $20 admission plus $1 for each ride. Write an inequality that would express the situation where plan B is the best buy,

Answer 1

Let x = # of rides

Plan A: 10 + 3x

Plan B: 20 + x

if x < 5 rides then plan A is better buy
if x = 5 both plans are the same
if x > 5 then plan B is the best buy

Prove:
x = 6 (rides)

plan A: 10 + 3x = 10 + 3(6) = 10+18 = $28
plan B: 20 + x = 20 + 6 = $26

Answer 2

`x+20<3x+10`

Explanation:

Let x represent the number of rides.

We have been given that a carnival has two payment options.

In Plan A, you pay $10 admission plus $3 for each ride. The total cost for x rides using plan A would be
`3x+10`.

In Plan B, you pay a $20 admission plus $1 for each ride.The total cost for x rides using plan B would be
`x+20`.

Now we will show that plan B is best buy by showing that cost of x rides in plan B is less than plan A as:

`x+20<3x+10`

Therefore, our required inequality would be
`x+20<3x+10`.