How do I solve this?

Question

Beginning in 2000, a sports team increased its ticket price by a constant amount each year until 2020.

• A ticket cost $62.25 in 2010 
• A ticket cost $76.5 in 2014 

How much did a ticket cost in 2020?

 

I do not know how to solve this, please show me how to solve step-by-step. Thank you.

 

 

Answer 1

2010:  price =$62.25

2014: price = $76.50

 

To get from 2010 price to 2014 price

we add the common difference 4 times. 

 

62.25 + 4d = 76.50

4d = 14.25

d = 14.25/4

d = 3.5625

 

Your common difference is $3.5625

(strange number..., but that's what the problem shows)

 

2020:

price = 2014 price + 6d

price = 76.50 + 6(3.5625)

price = 76.50 + 21.375

price = $97.875

Answer 2

Let X =Price in 2000

Let Y = increase every year

2001 it will be X +Y

2002 it will be X +2Y

2010 it should be X +10 Y =62.25 ... Eq 1

2014 it should be X +14 Y = 76.5...... Eq 2

Solving 4Y = 14.25 

Gives Y =$ 3.5625

X = $26.625

Value of ticket in 2020 = X + 20Y = $97.875

 

But the values appear to be unrealistic, except for years 2010 and 2014