Question

Your family buys tickets for the Ranger game. Each ticket costs $16. You also have to pay for parking. After buying 4 tickets, your total bill is $96.50.
a) How much did you pay for parking?
b) Write an equation that gives your total bill (in dollars) as a function of the number of tickets you buy. Be sure to define your variables!
c) How many tickets could you buy with $250 if you also have to pay for parking?​

Answer 1

Part (a)

Answer: $32.50

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Work Shown:

Each ticket costs $16. If you buy four of them, then you paid 4*16 = 64 dollars.

The total bill was $96.50

This leaves 96.50-64 = 32.50 for parking.

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Part (b)

Answer:  y = 16x+32.50

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Work Shown:

x = number of tickets

y = total bill (in dollars)

1 ticket costs 16 dollars

x tickets cost 16x dollars since we multiply both values by x

Add on the cost of parking to get a total bill of y = 16x+32.50

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Part (c)

Answer:  at most 13 tickets

In other words, 13 is the max you can get.

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Work Shown:

Plug y = 250 into the equation found back in part (b). Solve for x

We'll follow PEMDAS in reverse to isolate x

y = 16x+32.50

250 = 16x+32.50

16x+32.50 = 250

16x = 250-32.50

16x = 217.5

x = 217.5/16

x = 13.59375

Since we can't buy a fraction of a ticket, we must round down to the nearest whole number. We cannot round to x = 14 despite the value 13.59375 being closer to 14 as it is to 13.

x = 13 is the answer we're after.

If we plug in x = 13, we get

y = 16x+32.50 = 16*13+32.50 = 240.5

while x = 14 leads to

y = 16x+32.50 = 16*14+32.50 = 256.5

The first result of $240.50 is under $250 while the second result $256.50 is over $250. So that's why x = 13 is the largest number of tickets we can buy.