SOLUTION: Linda has $1.85 in quarters, nickels, and dimes. If she has three times as many dimes as quarters, and five fewer nickels than dimes, how many of each coin does she have?

Question 135410: Linda has $1.85 in quarters, nickels, and dimes. If she has three times as many dimes as quarters, and five fewer nickels than dimes, how many of each coin does she have?
Found 2 solutions by ankor@dixie-net.com, nycsharkman:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write an equation for each statement
:
Linda has $1.85 in quarters, nickels, and dimes.
.05n + .10d + .25q = 1.85
:
If she has three times as many dimes as quarters,
q = d/3
:
five fewer nickels than dimes,
n = (d - 5)
:
how many of each coin does she have?
:
Substitute (d/3) for q and (d-5) for n in the 1st equation:
:
.05(d-5) + .10d + .25(d/3) = 1.85
:
.05d - .25 + .10d +(.25d/3) = 1.85; multiplied what's inside the brackets
:
.05d + .10d + (.25d/3) = 1.85 + .25; add .25 to both sides
:
.15d + (.25d/3) = 2.10
:
.45d + .25d = 6.30; multiplied equation by 3
:
.70d = 6.30
:
d = 6.3/.7; divided both sides by .7
:
d = 9 dimes
:
nickels: 9 - 5 = 4 nickels (five fewer nickels than dimes,)
:
Quarters: 9/3 = 3 quarters (three times as many dimes as quarters,)
:
Check solutions:
.05(4) + .10(9) + .25(3) =
.20 + .90 + .75 = 1.85
Answer by nycsharkman(136) (Show Source): You can put this solution on YOUR website!
Linda has $1.85 in quarters, nickels, and dimes. If she has three times as many dimes as quarters, and five fewer nickels than dimes, how many of each coin does she have?
number of quarters = x
value of each quarter = 0.25
total = x(0.25)
===========================
number of nickels = x - 5
value of each nickle = 0.05
total = 0.05(3x - 5)
===========================
number of dimes = 3x
value of each dime = 0.10
total = 3x(0.10)
===========================
All the coins Linda has total $1.85.
We add all 3 totals and equate to Linda's total.
x(0.25)+ 0.05(3x - 5)+ 3x(0.10)= 1.85
Let's do away with the decimal by multiplying each decimal point by the number 100.
0.25 times 100 = 25
0.05 times 100 = 5
0.10 times 100 = 10
1.85 times 100 = 185
It's easier working without decimals.
We now have this equation WITHOUT decimnals:
x(25)+ 5(3x - 5)+ 3x(10)= 185
25x + 15x - 25 + 30x = 185
40x - 25 + 30x = 185
70x - 25 = 185
70x = 185 + 25
70x = 210
x = 210/70
x = 3
==========
Quarters:
x = 3
So, 3 quarters
Nickels:
3x - 5
3(3) - 5
9 - 5 = 4 nickels
Dimes:
3x
3(3) = 9 dimes

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