Question 60876
Let the cost of admission be: {{{C[A] = 18}}} and {{{C[C] = 8}}}
Let the number of adults = {{{A}}} and the number of children = {{{C}}}

Then {{{A + C = 21}}} as there were 21 people.
And {{{A*C[A] + C*C[A] = 288}}} as $288 was collected.

So, {{{18A + 8C = 288}}}

Since, {{{A + C = 21}}}, {{{C = 21 - A }}}

So, {{{18A + 8(21 - A) = 288}}}
Or, {{{18A + 168 - 8A = 288}}}
Or, {{{10A + 168 = 288}}}
Or, {{{10A = 120}}}
So, {{{A = 12}}}
So, There were 12 adults and since there were 21 people altogether there were 9 children.


Verify this answer by plugging in {{{A = 12}}} and {{{C = 9}}} in {{{A*C[A] + C*C[A] = 288}}}

{{{12 * 18 + 9 * 8}}} should = 288.
{{{12 * 18 = 216}}}
{{{9 * 8 = 72}}}
{{{216 + 72}}} does indeed = 288.