Question 401466
{{{d}}} = number of dimes
{{{q}}} = number of quarters
{{{h}}} = number of half-dollars
given:
(1) {{{10d + 25q + 50h = 1110}}} (in cents)
(2) {{{d + q + h = 42}}}
(3) {{{q = 2d}}}
There are 3 equation and 3 unknowns, so it's solvable
--------------------
Substitute (3) into (1):
(1) {{{10d + 25*(2d) + 50h = 1110}}}
(1) {{{10d + 50d + 50h = 1110}}}
(1) {{{6d + 5h = 111}}}
and
(2) {{{d + 2d + h = 42}}}
(2) {{{3d + h = 42}}}
Multiply both sides by {{{2}}} and subtract from (1) 
(1) {{{6d + 5h = 111}}}
(2) {{{-6d - 2h = -84}}}
{{{3h = 27}}}
{{{h = 9}}}
and, from (2):
{{{3d + 9 = 42}}}
{{{3d = 33}}}
{{{d = 11}}}
from (3):
{{{q = 2*11}}}
{{{q = 22}}}
There are 11 dimes, 22 quarters, and 9 half dollars
check answer:
(1) {{{10d + 25q + 50h = 1110}}}
{{{10*11 + 25*22 + 50*9 = 1110}}}
{{{110 + 550 + 450 = 1110}}}
{{{1110 = 1110}}}
OK