Question 1124778
Let {{{ x }}} = the number of quarters Quincy has originally
{{{ x + 5 }}} = the number of dimes Dirk has originally
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Natalie gives Dirk a nickel. His coins are worth:
{{{ 10*( x+5 ) + 5 }}} cents
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Dirk gives Quincy a dime.
Dirk痴 coins are worth:
{{{ 10*( x+5 ) + 5 - 10 }}}
Quincy痴 coins are worth:
{{{ 25x + 10 }}}
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Quincy gives Natalie a quarter
His coins are worth:
{{{ 25x + 10 - 25 }}}
Natalie:
She lost a nickel and gained a quarter, so
she is plus {{{ 20 }}} cents
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They all have the same amount now
{{{ 25x - 15 }}} is Quincy痴 amount
{{{ 10*( x+5 )  - 5 }}} is Dirk痴 amount
They all have the same amount, so
{{{ 25x - 15 = 10*( x + 5 ) - 5 }}}
{{{ 25x - 15 = 10x + 50 - 5 }}}
{{{ 15x = 60 }}}
{{{ x = 4 }}}
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Quincy had {{{ x = 4 }}} coins originally
Dirk had {{{  x+5 = 9 }}} coins originally
Natalie ended up with {{{ 25x - 15 = 85 }}} cents,
Which is {{{ 20 }}} cents more than she started with
She started with {{{ 65 }}} cents
She had nickels, so she started with
{{{ 65/5 = 13 }}} coins originally
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Get a 2nd opinion if needed