Question 1201132
<pre>
Formulate a system of equations for the situation below and solve.

A theater has a seating capacity of 750 and charges $4 for children, $6 for students, and $8 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $4600. How many children attended the show?
 ______children

Let number of children, students, and adults, be C, S, and A, respectively
Then we get: {{{matrix(3,6, C + S + A, "=", 750, "-----", eq, "(i)", 4C + 6S + 8A, "=", "4,600", "-----", eq, "(ii)", C + S, "=", 2A, "-----", eq, "(iii)")}}}

You requested the above!!

                  2A + A = 750 ----- Substituting 2A for C + S in eq (i)
                      3A = 750
 Number of adults, or {{{matrix(1,5, A, "=", 750/3, "=", 250)}}}
 
                   C + S = 2(250) --- Substituting 250 for A in eq (iii) 
                   C + S = 500
                       S = 500 - C -- eq (iv)

            4C + 6S + 8A = 4,600 ---- eq (ii)
4C + 6(500 - C) + 8(250) = 4,600 ---- Substituting 500 - C, and 250, for S and A, respectively, in eq (ii) 
 4C + 3,000 - 6C + 2,000 = 4,600
                 4C - 6C = 4,600 - 5,000
                    - 2C = - 400
<font color = blue><font size = 4><b>Number of children</font></font></b>, or {{{highlight_green(matrix(1,5, C, "=", (- 400)/(- 2), "=", highlight(200)))}}}</pre>