Question 462021
This is a system of equations. Let d=the number of dimes and n=the number of nickels.
{{{.10d+.05n=5.75}}}
{{{d+n=83}}} Solve this equation for d.
{{{d=83-n}}} Now take 83-n and substitute it into the first equation for d.
{{{.10(83-n)+.05n=5.75}}} Simplify and solve.
{{{8.3-.10n+.05n=5.75}}}
{{{8.3-.05n=5.75}}}
{{{-.05n=-2.55}}}
{{{n=51}}} 51 nickels. Since there are 83 coins altogether, then there must be 32 dimes.