Question 1158500
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$23.50 in change consisting of dimes, quarters, halves, and dollars with one third as many halves as dimes, twice as many quarters as dimes and 7 more dollars than halves
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d, q, h, D
dimes, quarters, half-dollars, DOLLARS


{{{system(10d+25q+50h+100D=2350,3h=d,q/d=2,D-h=7)}}}


{{{system(2d+5q+10h+20D=470,d=3h,q=2d,D=h+7)}}}


Substitute for D:

{{{2d+5q+10h+20h+140=470}}}

{{{2d+5q+30h=470}}}

{{{2d+5q+30h=330}}}

substitute for q:

{{{2d+5*2d+30h=330}}}

{{{12d+30h=330}}}

{{{highlight_green(2d+5h=55)}}}


Sub for d in that two-variable equation:
{{{6h+5h=55}}}

{{{11h=55}}}

{{{highlight(h=5)}}}
and from this find the numbers of the other coins.