Question 304101
Let {{{t}}} = number of hours she worked as a cashier last week
Then {{{t + 8}}} = number of hours she worked in diner
given:
{{{1200t}}} = earnings last week as cashier (in cents)
{{{635*(t + 8)}}} = earnings last week in diner
{{{1200t + 635*(t + 8) = 13275}}}
----------------------------
{{{1200t + 635t + 5080  = 13275}}}
{{{1835t = 13275 - 5080}}}
{{{1835t = 8195}}}
{{{t = 4.466}}}
{{{t + 8 = 12.466}}}
This comes out 4 hrs 28 min as cashier and 12 hrs 28 min at diner
check:
{{{1200t + 635*(t + 8) = 13275}}}
{{{1200*4.466 + 635*(4.466 + 8) = 13275}}}
{{{5359.2 + 635*12.466 = 13275}}}
{{{5359.2 +  7915.91 = 13275}}}
{{{13275.11 = 13275}}} (error due to rounding off)