Question 175616
treasurer has $28.45 consisting of nickels, dimes, and quarters.
 She has 9 more nickels than dimes and three times as many dimes as quarters.
 How many does she have of each coin?
:
Write an equation for each statement:
:
"treasurer has $28.45 consisting of nickels, dimes, and quarters."
.05n + .10d + .25q = 28.45
:
 "She has 9 more nickels than dimes"
n = d + 9
:
" and three times as many dimes as quarters."
d = 3q
or we can write it:
q = {{{1/3}}}d
:
 How many does she have of each coin?
:
Using the 1st equation substitute:
(d+9) for n
{{{1/3}}}d for q
.05(d+9) + .10d + .25({{{1/3}}}d) = 28.45
.05d + .45 + .10d + {{{.25/3}}}d = 28.45
.15d + {{{.25/3}}}d = 28.45 - .45
.15d + {{{.25/3}}}d = 28.00
Multiply equation by 3 to get rid of the denominator
.45d + .25d = 84
.70d = 84
d = {{{84/.7}}}
d = 120 dimes
:
Find nickels:
n = 120 + 9
n = 129 nickels
:
Find quarters:
q = {{{1/3}}}*120
q = 40 quarters
;
:
Check solutions in the 1st equation:
.05(129) + .10(120) + .25(40) = 
6.45 + 12.00 + 10.00 = 28.45; confirms our solutions