Question 1151939

an art museum sold 63 tickets in 30 minutes. The ratio of adult to child tickets was 5:1. The ratio of adult to senior tickets was 5:3. How many of each kind of ticket were sold?
<pre>Let number of children, adults, and seniors be C, A, and S, respectively
Since children to adults, or C:A = 1:5, it follows that: {{{matrix(1,10, C/A, "=", 1/5, "_____", A, "=", 5C, "---------", eq, "(i)")}}}
Since adults to seniors, or A:S = 5:3, then {{{matrix(1,3, A/S, "=", 5/3)}}}
                                            {{{matrix(1,3, 5C/S, "=", 5/3)}}} ------ Replacing A with 5C
                                            5S = 3(5C) ---- Cross-multiplying
                                            {{{matrix(1,5, S, "=", 3(5C)/5, "=", 3C)}}}
With total number of attendees being 63, we then get: C + A + S = 63, or C + 5C + 3C = 63
                                                                         9C = 63
                                                                         C, or {{{highlight_green(matrix(1,7, Number, of, children, "=", 63/9, "=", 7))}}}
                                                                         {{{highlight_green(matrix(1,6, Number, of, "adults:", 5(7), "=", 35))}}}
                                                                         {{{highlight_green(matrix(1,8, Number, of, "seniors:", 3(7), "or", 63 - (7 + 35), "=", 21))}}}