SOLUTION: My question is this: Lotty has $5 in nickles,dimes, and quarters. She has 3 times as many nickles as dimes. She has 5 times as much money in quarters as she does in nickles. How mu

Question 343869: My question is this: Lotty has $5 in nickles,dimes, and quarters. She has 3 times as many nickles as dimes. She has 5 times as much money in quarters as she does in nickles. How much of each does she have? (btw...the answer I got was that she would have 5 dimes, 15 nickels, and 15 quarters...but again, I got that with trial and error...they add up right but i dont know how to write an equation to show how to get those as answers...)So, I guess the thing I need help with is trying to find an equation to show how I got my answers. If you could help me, I would really appreciate it! Thank you.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Here is the algebra way, write an equation for each statement
:
n = no. of nickels, d = no. of dimes, q = no. of quarters
:
"Lotty has $5 in nickles,dimes, and quarters."
.05n + .10d + .25q = 5.00
:
We will try to get everything in terms of n
:
"She has 3 times as many nickles as dimes."
n = 3d
Divide both sides by 3
d = n
:
"She has 5 times as much money in quarters as she does in nickles."
.25q = 5(.05n)
.25q = .25n
q =
q = n
:
Using the 1st equation, replace d with n, replace q with n
.05n + .10(n) + .25n = 5.00
:
get rid of the fraction, multiply each term by 3, results:
.15n + .10n + .75n = 15.00
1n = 15
n = 15 nickels
we know q = n,
q = 15 quarters
and
d = (15)
d = 5 dimes

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