Question 341951
Jody has a collection of 116 coins consisting of dimes, quarters, and silver dollars.
d + q + $ = 116
:
 The number of quarters is 5 less than three-fourths the number of dimes.
q = {{{3/4}}}d - 5
:
 The number of silver dollars is 7 more than five-eighths the number of dimes.
$ = {{{5/8}}}d + 7
:
How many coins of each kind are in her collection?
Using the 1st equation replace q & $
d + {{{3/4}}}d - 5 + {{{5/8}}}d + 7 = 116
Common denominator
d + {{{6/8}}}d + {{{5/8}}}d + 2 = 116
d + {{{11/8}}}d = 116 - 2
d + {{{11/8}}}d = 114
Multiply by 8 to get rid of the denominator, results:
8d + 11d = 912
d = {{{912/19}}}
d = 48 dimes
then
q = {{{3/4}}}(48) - 5
q = 36 - 5
q = 31 quarters
and
$ = {{{5/8}}}(48) + 7 
$ = 37 silver dollars
:
Check total: 48 + 31 + 37 = 116