Question 933517
 

{{{nickels=n}}}, 
{{{dimes=d}}}, and 
{{{quarters =q}}}

given:
{{{n+d+q=80}}} .....eq.1

if the nickels and the quarters are worth ${{{4.50}}} 

{{{0.05n+0.25q=4.50}}} .....eq.2

the value of the quarters and the dimes is ${{{5.50}}}

{{{0.25q+0.10d=5.50}}} .....eq.3


solve the system:
{{{n+d+q=80}}} .....eq.1
{{{0.05n+0.25q=4.50}}} .....eq.2
{{{0.25q+0.10d=5.50}}} .....eq.3
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{{{0.05n+0.25q=4.50}}} .....eq.2...multiply by {{{100}}}
{{{0.25q+0.10d=5.50}}} .....eq.3...multiply by {{{100}}}
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{{{5n+25q=450}}} .....eq.2
{{{25q+10d=550}}} .....eq.3
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{{{n+d+q=80}}} .....eq.1..solve for {{{n}}}

{{{n=80 -d-q}}}.......substitute in eq.2


{{{5(80 -d-q)+25q=450}}} .....eq.2 ...

{{{400 -5d-5q+25q=450}}}

{{{ 20q-5d+400 = 450}}}

{{{ 20q-5d=50}}}...solve for {{{d}}}

{{{ 20q-50=5d}}}

{{{ 20q/5-50/5=5d/5}}}

{{{ d=4q-10}}}...................


go to {{{25q+10d=550}}} .....eq.3....substitute {{{d}}}

{{{25q+10(4q-10)=550}}} 

{{{25q+40q-100=550}}} 

{{{65q=550+100}}}

{{{65q=650}}}

{{{q=650/65}}}

{{{highlight(q=10)}}}



go to {{{ d=4q-10}}}. ........substitute {{{q}}} and find {{{d}}}

{{{ d=4*10-10}}}

{{{ d=40-10}}}

{{{highlight( d=30)}}}

go to 
{{{n=80 -d-q}}}.......substitute {{{q}}} and {{{d}}}, find {{{n}}}

{{{n=80 -30-10}}}

{{{highlight( n=40)}}}