Question 629105
Mary has $2.25 in coins. She has the same number of quarters as dimes.
 She has half as many as nickels as quarters
How many of each coin does she have?
let n = no. nickels
let d = no. dimes
let q = no. quarters
;
Write an equation for each statement
:
"Mary has $2.25 in coins."
.05n + .10d + .25q = 2.25
:
"She has the same number of quarters as dimes.'
q = d
:
"She has half as many as nickels as quarters"
n = .5q
:
In the first equation, replace n with .5q; replace d with q
.05(.5q) + .10q + .25q = 2.25
.025q + .10q + .25q = 2.25
.375q = 2.25 
q = 2.25/.375
q = 6 quarter
then
d = 6 dimes
and
n = 3 nickels
:
Check .05(3) + .10(6) + .25(6) = 2.25
:
:
2. "Sue has twice as many quarters as nickels"
q = 2n
"and half as many dimes as nickels."
d = .5n
"If she has a total of $4.80,"
.05n + .10d + .25q = 4.80
Replace d and q
.05n + .10(.5n) + .25(2n) = 4.80
.05n + .05n + .50n = 4.80
.60n = 4.80
n = 4.80/.60
n = 8 nickels
then
d = 4 dimes
and
q = 16 quarters
:
You can check the total$ with these solutions