Jen Butler has been pricing​ Speed-Pass train fares for a group trip to New York.Three adults and four children must pay $104. Two adults and three children must pay $73.

Question

Find the price of the adult's ticket and the price of a child's ticket.

Answer 1

The variables are:

A = Adult Ticket

C = Child Ticket

This gives us two equations:

3A + 4C = 104

2A + 3C = 73

First, we eliminate C and solve for A by multiplying the first equation by 3 and the second equation by -4:

3(3A + 4C = 104)

= 9A + 12C = 312

-4(2A + 3C = 73)

= -8A -12C = -292

Now, add the equations to eliminate C:

9A + 12C = 312

-8A - 12C = -292

A = 20

Now we know an adult ticket costs $20. Next, plug 20 into one of the original equations to solve for C:

2(20) + 3C = 73

3C = 33

C = 11

So, an Adult ticket is $20 and a Child ticket is $11

Answer 2

First, let us define some variables.

Let:

-The price for an adult be "A"

-The price for a child be "C"

We will now organize the given information into a system of equations.

(eq. 1)......... 3*A+4*C=$104 [3 adults and 4 children must pay $104]

(eq. 2)......... 2*A+3*C=$73 [2 adults and 3 children must pay $73]

Next, isolate one of the variables (let's do adults "A") for one of the equations (let's us equation 1).

We will subtract the quantity "4*C"to each side of the equation:

3*A+4*C-4*C=$104-4*C

3*A=$104-4*C

Then we will divide both sides of the equation by "3":

(3*A)/3=($104-4*C)/3

(eq. 3)..........A=($104-4*C)/3

We can now substitute equation 3 into equation 2:

2*[($104-4*C)/3]+3*C=$73

Solve for C by multiplying both sides of the equation by 3:

3*{2*[($104-4*C)/3]+3*C}=3*($73)

This leaves us with:

2*($104-4*C) + 9*C=$219

Distributing the 2 gives us:

$208 - 8*C + 9*C = $219

Combining like-terms gives us:

-8*C+9*C= $219 - $208

When simplified is:

C=$11

Having found the price of admission for a child ($11), we can now substitute this value into equation 3:

A= ($104-4*C)/3, with C= $11

A= ($104 - 4 * $11)/3

A= ($104 - $44)/3

A= ($60)/3

A= $20

Final Answer:

Price of Adult Ticket- $20

Price of Child Ticket- $11