Math Problem I don't understand.. details inside?

Question

Find the number of the round-trip computer tickets sold.

Hints.

[1] Thirty times as many round-trip tickets as 12- ride tickets were sold

[2] The total number of tickets sold represented 1440 rides

A chart made in a few seconds on paint is here: http://i7.photobucket.com/albums/y284/alvintheninja/random/arthurshw.jpg

Serious answers please.. I've also tried to ask everyone else in my household.

Answer 1

First, assign variables to everything:

Let R = number of Round-Trip Tickets sold
Let X = number of 12-ride tickets sold

Now, what do we know?

(1) "30 times as many round-trip tickets as 12-ride tickets were sold" so we would have to sell 30 times as many 12-ride tickets to equal the number of round-trip tickets:

R = 30X

(2) "total number of tickets sold represents 1440 rides" -- assuming two rides per round-trip ticket [one out and one back] and 12 rides on each 12-ride ticket, this means:

2R + 12X = 1440

That means you can express R in terms of X:

if 2R + 12X = 1440, then
R + 6X = 720 (dividing both sides by 2)
R = 720 - 6X

Now, plug that back into expression (1):

(720-6X) = 30X
720 - 6X = 30X

Get all terms in on the same side of the equation:

720 = 30X + 6X
720 = 36X

divide both sides by the multiple of X so we can find the value of 1X:

720 / 36 = 36X / 36
20 = X

So, we sold 20 12-ride tickets. Now plugging that value back into equation (1) we get:

R = 30X
R = 30 * 20
R = 600

We sold 600 round-trip tickets.

Then to make sure we did it right, double-check that the fist known equation is correct:

"total number of tickets sold represents 1440 rides" -- assuming two rides per round-trip ticket [one out and one back] and 12 rides on each 12-ride ticket, this means:

2R + 12X = 1440
2*600 + 12*20 = 1440 ?
1200 + 240 = 1440 ?
1440 = 1440 ? *** YES ***

So we have the right answer.

Answer 2

Continuing, T = total no of rides = 2*rounders + 12*(twelvers)

(Two rides per round trip, 12 rides per 12-ride ticket)

rounders = 30*(twelvers)

2*30*(twelvers) + 12*(twelvers) = 1440

twelvers = 1440/(2*30+12)

rounders = (30*1440)/(2*30+12)