Question 629105: 1. 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?
2. Sue has twice as many quarters as nickels and half as many dimes as nickels. If she has a total of $4.80, how many of each coin does she have?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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
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