Question 168521
Let {{{p}}}= the number of pennies
Let {{{n}}}= the number of nickels
Let {{{d}}}= the number of dimes
Given:
(1){{{p + 5n + 10d = 840}}} (in cents)
(2){{{d = 2p - 6}}}
(3){{{d = n}}}
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From (2), 
{{{2p - 6 = d}}}
{{{2p = d + 6}}}
{{{p = (1/2)*d + 3}}}
Substitute in (1)
{{{p + 5n + 10d = 840}}}
{{{(1/2)*d + 3 + 5d + 10d = 840}}}
{{{(1/2)*d + 15d + 3 = 840}}}
Multiply both sides by {{{2}}}
{{{d + 30d + 6 = 1680}}}
{{{31d = 1674}}}
{{{d = 54}}}
{{{n = 54}}}
There are 54 nickels in the jar
Also,
{{{p = (1/2)*d + 3}}}
{{{p = (1/2)*54 + 3}}}
{{{p = 30}}}
Now check answer:
{{{p + 5n + 10d = 840}}}
{{{30 + 5*54 + 10*54 = 840}}}
{{{30 + 270 + 540 = 840}}}
{{{840 = 840}}}
OK