Question 1060552
For simple interest, and also
for 1 year:
{{{ I = P*r*t }}}
where {{{ P }}} is the amount invested 
at rate {{{ r }}}
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{{{ I[1] = P*.08*1 }}}
{{{ I[2] = 2P*.09*1 }}}
{{{ I[3] = 3P*.1*1 }}}
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{{{ I[1] + I[2] + I[3] = 112 }}}
{{{ .08P + .18P + .3P = 112 }}}
{{{ .56P = 112 }}}
{{{ P = 200 }}}
{{{ 2P = 400 }}}
{{{ 3P = 600 }}}
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$200 is invested at 8%
$400 is invested at 9%
$600 is invested at 10%
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Let {{{ t }}} = the number of hours she worked 
for the week
{{{ 471.5 = 11.5*35 + 17.25*( t - 35 ) }}}
{{{ 471.5 = 402.5 + 17.25t - 603.75 }}}
{{{ 17.25t = 471.5 + 603.75 - 402.5 }}}
{{{ 17.25t = 69 + 603.75 }}}
{{{ 17.25t = 672.75 }}}
{{{ t = 39 }}}
She worked 39 hrs for the week
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check:
{{{ 471.5 = 11.5*35 + 17.25*( t - 35 ) }}}
{{{ 471.5 = 11.5*35 + 17.25*( 39 - 35 ) }}}
{{{ 471.5 = 402.5 + 69 }}}
{{{ 471.5 = 471.5 }}}
OK