Question 941032
Let {{{ b }}} = the number of bricks in the wall
Jack's rate:
{{{ b/8 }}}
Danny's rate:
{{{ b/11 }}}
---------------
{{{ b/8 + b/11 = ( b+7 )/5  }}}
{{{ (5/8)*b + (5/11)*b = b + 7 }}}
Multiply both sides by {{{ 88 }}}
{{{ 55b + 40b = 88b + 616 }}}
{{{ 95b - 88b = 616 }}}
{{{ 7b = 616 }}}
{{{ b = 88 }}}
--------------
There are {{{ 88 }}} bricks in the wall
check:
{{{ b/8 + b/11 = ( b+7 )/5  }}}
{{{ 88/8 + 88/11 = ( 88+7 )/5  }}}
{{{ 11 + 8 = 95/5 }}}
{{{ 19 = 19 }}}
OK
----------------
I was confused about whether to add or subtract
the {{{ 7 }}} in {{{ b/8 + b/11 = ( b+7 )/5  }}}
The only way the equation can work is if I add
the {{{ 7 }}}. I can force myself to make sense of it
if I say that {{{ b+7 }}} has to be the "normal" rate
for them working together, and the {{{ 7 }}} makes
up for their loss of rate. Hope I got this- definitely
get another opinion.