Question 420062
Let cost of a hamburger  = {{{a}}}
Let cost of a hot dog = {{{b}}}
given:
(1) {{{ 5a + 3b = 2425 }}} (in cents)
(2) {{{ 3a + 5b = 2175 }}} (in cents)
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Multiply (1) by {{{3}}} and (2) by {{{5}}}
(1) {{{ 15a + 9b = 7275 }}} 
(2) {{{ 15a + 25b = 10875 }}} 
Subtract (1) from (2)
(2) {{{ 15a + 25b = 10875 }}} 
(1) {{{ -15a - 9b = -7275 }}} 
{{{ 16b = 3600 }}}
{{{ b = 225 }}}
Plug this into (2)
(2) {{{ 3a + 5*225 = 2175 }}} 
{{{ 3a + 1125  = 2175 }}}
{{{ 3a = 1050 }}}
{{{a = 350 }}}
The price of a hamburger is $3.50
check:
(1) {{{ 15a + 9b = 7275 }}} 
(1) {{{ 15*350 + 9*225 = 7275 }}}
(1) {{{ 5250 + 2025 = 7275 }}} 
(1) {{{ 7275 = 7275 }}}
OK