Question 1109593
Let {{{ a }}} = the price of a senior ticket
Let {{{ b }}} = the price of a student ticket
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(1) {{{ 10a +1*b = 54 }}}
(2) {{{ 1*a + 5b = 74 }}}
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Multiply both sides of (1) by {{{ 5 }}}
and subtract (2) from (1)
(1) {{{ 50a + 5b = 270 }}}
(2) {{{ -a - 5b = -74 }}}
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{{{ 49a = 196 }}}
{{{ a = 4 }}}
and
(1) {{{ 10*4 + b = 54 }}}
(1) {{{ 40 + b = 54 }}}
(1) {{{ b = 14 }}}
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A senior ticket costs $4
A student ticket costs $14
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check:
(2) {{{ a + 5b = 74 }}}
(2) {{{ 4 + 5*14 = 74 }}}
(2) {{{ 4 + 70 = 74 }}}
(2) {{{ 74 = 74 }}}
OK