Question

A movie theater sends out a coupon for 95​% off the price of a ticket. Write an equation for the​ situation, where y is the price of the ticket with the​ coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant.

Answer 1

y = 0.05x

Explanation:

A movie theater sends out a coupon for 95​% off the price of a ticket, so the price of the ticket with the​ coupon is 100% - 95% = 5% of the original price.

Let

x = original price

y = price of the ticket with the​ coupon

Then

x - 100%

y - 5%

Write a proportion:

`(x)/(y)=(100)/(5)`

Cross multiply:

`100y=5x\\ \\y=0.05x`

Since the original price and final price are always greater than 0, then the graph of this equation is in the first quadrant (see attached diagram)