Question 110805


Let:

{{{Quarters = q}}} 
{{{Dimes = d}}} 
{{{Nickels = n}}}

If nine times as many dimes as quarters, then …  => {{{9d = q }}}

If five times as many nickels as quarters, then … => {{{5n = q}}}

If machine contains ${{{2100}}} worth of {{{quarters}}}, {{{dimes}}}, and {{{nickels}}}, then:

{{{2100 = q*.25 + d*.10 + n*.05 }}}

Since 

{{{d = 9q }}} and {{{n = 5q}}}, we will have:


{{{2100 = q*.25 + 9q*.10 + 5q*.05 }}}..........all represented in dollars


{{{2100 = q*.25 + q*.9q + .25q }}}

{{{2100 = q (.25 + .9 + .25)}}}

{{{2100 = 1.4q}}}

{{{2100/1.4 = q}}}


{{{q = 1500}}}……………………………….number of quarters


{{{d = 9*1500 = 13500}}}………………….. number of dimes

and {{{n = 5*1500= 7500}}},………………. number of  nickels


check:

{{{2100 = 1500.25 + 13500.10 + 7500.05 }}}

{{{2100 = 375+ 1350+ 375}}}

{{{2100 = 2100}}}