Question

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At a local movie theater, the price for tickets is $10.00 for adults and $5.50 for students. The price of adult tickets increases by $0.20 each year, and the price of student tickets increase
$0.50 each year. The equations y = 0.20z+10 and y=0.5z +5.5 represent the situation, where x represents the number of years since the first year, and y represents the price of
tickets. After how many years will the ticket prices be the same? after how many years.

Answer 1

So ticket prices will be the same after 15 years

Explanation:

Set the two equations right side equal to each other and solve for x

0.5x +5.5 = 0.20x + 10

Subtract 0.2x from both sides

0.5x - 0.2x + 5.5 = 0.2x - 0.2x + 10

0.3x + 5.5 = 10

Subtract 5.5 from both sides:
0.3x + 5.5 - 5.5 = 10 - 5.5

0.3x = 4.5

Multiply by 10 for easier computation
10 x 0.3x = 10 x 4.5

3x = 45

Divide by 3 to get

3x/3 = 45/3

x = 15

So ticket prices will be the same after 15 years