Question 343869
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 = {{{1/3}}}n
:
"She has 5 times as much money in quarters as she does in nickles."
.25q = 5(.05n)
.25q = .25n
q = {{{(.25n)/.25}}}
q = n 
:
Using the 1st equation, replace d with {{{1/3}}}n, replace q with n
.05n + .10({{{1/3}}}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 = {{{1/3}}}(15)
d = 5 dimes