Question 507623
Call the numbers {{{x}}} and {{{y}}}
given:
(1) {{{ x = 5y + 2 }}}
(2) {{{ x*y = 24 }}}
Substitute (1) into (2)
(2) {{{ (5y + 2)*y = 24 }}}
(2) {{{ 5y^2 + 2y - 24 = 0 }}}
Use the quadratic formula
{{{y = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 5 }}}
{{{ b = 2 }}}
{{{ c = -24 }}}
{{{y = (-2 +- sqrt( 2^2-4*5*(-24) ))/(2*5) }}} 
{{{y = (-2 +- sqrt( 4 + 480 ))/ 10 }}} 
{{{y = (-2 +- sqrt( 484 ))/ 10 }}} 
{{{ y = (-2 + 22) / 10 }}}
{{{ y = 2 }}}
and, since
{{{ x = 5y + 2 }}}
{{{ x = 5*2 + 2 }}}
{{{ x = 12 }}}
The numbers are 12 and 2
(2)
Subtract the cost of parts from max and min
{{{ 226 - 175 = 51 }}}
{{{ 294 - 175 = 119 }}}
The mechanic works at least {{{ 51/34 = 1.5 }}} hrs
and, at the most, {{{ 119/34 = 3.5 }}} hrs
----------
Note that ( dollars ) / ( dollars per hr ) = hours