Question 703303
Let {{{ c }}} = number of Child's tickets
Let {{{ a }}} = number of adult tickets
Let {{{ s }}} = number of senior tickets
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(1) {{{ c/a = 4/7 }}}
(2) {{{ a/s = 7/1 }}}
(3) {{{ c/s = 4/1 }}}
(4) {{{ c + a + s = 144 }}}
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(1) {{{ c = (4/7)*a }}}
(2) {{{ s = (1/7)*a }}}
Substitute these results into (4)
(4) {{{ c + a + s = 144 }}}
(4) {{{ (4/7)*a + a + (1/7)*a = 144 }}}
(4) {{{ (12/7)*a  = 144 }}}
(4) {{{ a = (7/12)*144 }}}
(4) {{{ a = 84 }}}
and
(1) {{{ c = (4/7)*a }}}
(1) {{{ c = (4/7)*84 }}}
(1) {{{ c = 48 }}}
and
(2) {{{ s = (1/7)*a }}}
(2) {{{ s = (1/7)*84 }}}
(2) {{{ s = 12 }}}
48 child , 84 adult, 12 senior tickets