Question 720847

Let {{{ n }}} = number of nickels
Let {{{ N}}} = number of quarters
given:

{{{ N + n = 34 }}}....eq.1

{{{  0.25N +0.05n= 5.30 }}}....eq.2
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solve ....eq.1  for {{{ N }}}

{{{ N = 34-n }}}

and substitute it in  ....eq.2

{{{ 0.25(34-n) +0.05n= 5.30 }}}....eq.2...solve for {{{ n }}}

 {{{ 8.5- 0.25n+0.05n= 5.30 }}}

{{{ 8.5- 0.20n= 5.30 }}}

{{{ 8.5- 5.30 =0.20n}}}

{{{ 3.2 =0.20n}}}

{{{ n=3.2 /0.20}}}

{{{ n=16}}}

and, since

{{{ N + n = 34 }}}

{{{ N + 16 = 34 }}}

{{{ N = 34 -16}}}

{{{ N = 18}}}

The number of nickels is {{{16}}}
The number of quarters is {{{18}}}

check:

{{{ N + n = 34 }}}....eq.1

{{{ 18+ 16= 34 }}}

{{{ 34= 34 }}}

{{{  0.25N +0.05n= 5.30 }}}....eq.2

{{{  0.25*18 +0.05*16= 5.30 }}}

{{{  4.50 +0.80= 5.30 }}}

{{{  5.30= 5.30 }}}