Question 884473
{{{T}}} - number of ten dollar bills
{{{F}}} - number of five dollar bills
{{{Z}}} - number of one dollar bills
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.
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1.{{{10T+5F+Z=446}}}
2.{{{T+F+Z=94}}}
3.{{{F=10+T}}}
Substitute eq. 3 into eqs. 1 and 2,
{{{10T+5(10+T)+Z=446}}}
{{{10T+50+5T+Z=446}}}
4.{{{15T+Z=396}}}
.
.
{{{T+(10+T)+Z=94}}}
5.{{{2T+Z=84}}}
Subtract eq. 5 from eq. 4,
{{{15T+Z-2T-Z=396-84}}}
{{{13T=312}}}
{{{highlight(T=24)}}}
Then backsubstituting,
{{{15(24)+Z=396}}}
{{{360+Z=396}}}
{{{highlight(Z=36)}}}
and finally,
{{{F=10+24}}}
{{{highlight(F=34)}}}