Question 283672
In this word problem, I pulled out two equations:

Three adults and four children pay 122:

a = adults
c = children

3a + 4c = 122


Two adults and three children pay 87:

2a + 3c = 87

I used the Elimination Method to solve by subtracting the equations:

{{{3a+4c=122-2a+3c=87}}}


Better form this way, Subtract:
3a + 4c = 122
2a + 3c = 87 

a + c = 35

Now you can subtract one of the variables to the other side to get one by itself, either variable is fine:
{{{a + c = 35}}}
{{{c = 35 - a}}}

Now place the value of c into the first equation:

{{{3a + 4(35-a) = 122}}}
{{{3a + 140 - 4a = 122}}}
Combine the a's (like terms)

{{{-a + 140 = 122}}}
Subtract the 140 from the left to the right side of the equation:

{{{-a = 122-140}}}

{{{-a = -18}}}
Divide by a negative 1 to get a positive and to both sides:

{{{-a/-1 = -18/-1}}}

{{{a = 18}}}

Now you have the value of tickets for adults. You can place the value of a into the second equation to solve for c. 

{{{2(18) + 3c = 87}}}
{{{36 + 3c = 87}}}
 Subtract the 36 from the left to right side of the equation:

{{{3c = 87 - 36}}}
{{{3c = 51}}}

Divide 3 into itself and the right side:

{{{3c/3 = 51/3}}}
{{{c = 17}}}

If you Check: adults = 18, children = 17

Place the values into the first equation:

{{{3(18) + 4(17) = 122}}}
{{{54+68=122}}}
{{{122=122}}}