Question 697166
Revenues from the cheapest tickets is 
(1) {{{ n*x }}}
Revenues from the middle price tickets is 
(2) {{{ (n/3)*(3x) }}}
(2) {{{ n*x }}}
Revenues from the most expensive tickets is 
(3) {{{ (3/5)*(n/3)*(3/2)*(3x) }}}
(3) {{{ (9/10)*n*x }}}
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given:
{{{ n + n/3 + (3/5)*(n/3) = 690 }}}
{{{ n + n/3 + n/5 = 690 }}}
{{{ 15n + 5n + 3n = 690 }}}
{{{ 23n = 690 }}}
{{{ n = 30 }}}
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30 people buy the cheapest ticket
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given:
{{{ 1957.5 = n*x + n*x + (9/10)*n*x }}}
{{{ 1957.5 = (20/10)*n*x + (9/10)*n*x }}}
{{{ 1957.5 = 2.9*n*x }}}
{{{ 1957.5 = 2.9*30*x }}}
{{{ x = 1957.5 / 87 }}}
{{{ x = 22.5 }}}
What is the cost of the most expensive ticket?
{{{ (9/2)*x = (9/2)*22.5 }}}
{{{ (9/2)*x = 101.25 }}}
The cost of most expensive ticket is 101.25 pounds
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check answers:
(1) {{{ n*x = 30*22.5 }}}
(1) {{{ n*x = 675 }}}
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(2) {{{ n*x = 675 }}}
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(3) {{{ (9/10)*n*x = .9*30*22.5 }}}
(3) {{{ (9/10)*n*x = 607.5 }}}
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{{{ 2*675 + 607.5 = 1350 + 607.5 }}}
{{{ 2*675 + 607.5 = 1957.5 }}}
OK