Zoe, Minh, and Jake sold some tickets for a school fundraiser. Each ticket cost $2. Zoe sold 1/2 of the tickets. Minh and Jake sold the remaining tickets in the ratio 1:3. If Zoe sold 36 more tickets than Minh, how much money dis the 3 students collect altogether?

tickets sold by Minh --- x

tickets sold by Jake --- 3x
(notice x : 3x = 1 : 3)

So number of tickets sold by Zoe = 4x

4x - 36 = x
3x = 36
x = 12

total tickets = x+3x + 4x = 8x or 96
money collected = 96($2) = $192

Well, it seems like Zoe was quite the ticket-selling superstar, selling half of them! Meanwhile, poor Minh and Jake had to split the remaining tickets in a 1:3 ratio.

Let's say Zoe sold x tickets. That means Minh and Jake sold a total of (1/2)x tickets.

Now, here's the tricky part. We know that Zoe sold 36 more tickets than Minh. So we can set up an equation:

x = (1/2)x + 36

Now let's solve for x.

Subtracting (1/2)x from both sides, we get:

(1/2)x = 36

Now, multiplying both sides by 2:

x = 72

So, Zoe sold 72 tickets.

Now, let's find out how many tickets Minh and Jake sold.

If Zoe sold 72 tickets, that means Minh and Jake sold (1/2)x = (1/2) * 72 = 36 tickets.

Now, let's calculate the total amount of money collected by the three students:

Zoe collected 72 tickets * $2 per ticket = $144.

Minh and Jake sold a total of 36 tickets * $2 per ticket = $72.

So, altogether, the three students collected $144 + $72 = $216.

That's a whole lot of ticket-slinging and fundraising!

Let's denote the number of tickets sold by Zoe as Z. Since Zoe sold half of the tickets, this means that Minh and Jake sold the other half of the tickets, so the total number of tickets sold is 2Z.

We also know that Zoe sold 36 more tickets than Minh, so Z = M + 36.

Minh and Jake sold the remaining tickets in the ratio 1:3, which means that Minh sold 1/4 of the total tickets and Jake sold 3/4 of the total tickets. We can write this as:

M = (1/4) * 2Z = Z/2
J = (3/4) * 2Z = 3Z/2

Now, let's substitute the value of Z from the first equation into the second equation to find the values of M and J.

M = Z/2 = (M + 36)/2
2M = M + 36
M = 36

Now we can substitute the value of M into the equation for Z to find the value of Z.

Z = M + 36
Z = 36 + 36
Z = 72

So, Zoe sold 72 tickets, Minh sold 36 tickets, and Jake sold 3Z/2 = 3*72/2 = 108 tickets.

The total number of tickets sold is 72 + 36 + 108 = 216.

Each ticket cost $2, so the total amount of money collected is 216 * $2 = $432.

To find the answer, we need to break down the problem into steps:

Step 1: Find the total number of tickets sold by Zoe.
Since Zoe sold 1/2 of the tickets, and the ratio of Minh and Jake is 1:3, we can say that Zoe sold 1 part out of 4 parts (1 + 3) in total. Let's represent the total number of tickets as x.
So, Zoe sold (1/4) * x tickets.

Step 2: Find the total number of tickets sold by Minh and Jake.
Since Zoe sold 36 more tickets than Minh, we can say that Minh sold (1/4) * x - 36 tickets.

Now, the remaining tickets (3/4) * x - Minh's tickets must be equal to Jake's tickets.
So, (3/4) * x - (1/4) * x + 36 = (3/4) * x - Minh's tickets.
Simplifying the equation, we get (1/2) * x + 36 = Minh's tickets.

Step 3: Calculate the total number of tickets.
Since Zoe sold (1/4) * x tickets, Minh sold (1/2) * x + 36 tickets, and Jake sold the remaining tickets, we can add them up to find the total number of tickets sold.
Total tickets sold = (1/4) * x + (1/2) * x + 36 + x
= (7/4) * x + 36

Step 4: Calculate the total amount collected.
Since each ticket costs $2, we can multiply the total number of tickets by $2 to find the total amount collected by the three students.
Total amount collected = (7/4) * x + 36 * 2
= (7/4) * x + 72

Now we have the equation for the total amount collected by the three students. To find the numerical value, we need to know the value of x, which represents the total number of tickets sold.