Question 330373
Let D be the number of dimes, N nickels, Q quarters.
{{{D=2N}}}
{{{N=D/2}}}
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{{{Q=D-12}}}
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{{{5N+10D+25Q=900}}}
Substitute from above,
{{{(5D)/2+10D+25(D-12)=900}}}
Multiply both sides by 2.
{{{5D+20D+50D-600=1800}}}
{{{75D=2400}}}
{{{D=32}}}
{{{Q=32-12=20}}}
{{{N=32/2=16}}}
She has 16 nickels, 32 dimes, and 20 quarters.