SOLUTION: sarah has a collection of 80 coins made up of nickels, dimes. and quarters. she has 5 more dimes than one-third the number of nickels, and the number of quarters is one less than o

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Question 468330: sarah has a collection of 80 coins made up of nickels, dimes. and quarters. she has 5 more dimes than one-third the number of nickels, and the number of quarters is one less than one-fourth the number of nickels. how many coins of each kind does she have?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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sarah has a collection of 80 coins made up of nickels, dimes. and quarters.
she has 5 more dimes than one-third the number of nickels, and the number of
quarters is one less than one-fourth the number of nickels.
how many coins of each kind does she have?
:
Let n = no. of nickels
Let d = no. of dimes
Let q = no. of quarters
:
Write an equation for each statement:
"sarah has a collection of 80 coins made up of nickels, dimes. and quarters."
n + d + q = 80
:
"she has 5 more dimes than one-third the number of nickels,"
d = 1%2F3n + 5
:
" the number of quarters is one less than one-fourth the number of nickels."
q = 1%2F4n - 1
:
Replace d and q from the above equations:
n + (1%2F3n + 5) + (1%2F4n - 1) = 80
:
n + 1%2F3n + 1%2F4n - 1 + 5 = 80
:
n + 1%2F3n + 1%2F4n + 4 = 80
:
n + 1%2F3n + 1%2F4n = 80 - 4
:
n + 1%2F3n + 1%2F4n = 76
Get rid of those annoying fractions multiply by 12
12n + 4n + 3n = 12(76)
19n = 912
n = 912%2F19
n = 48 nickels
then
d = 1%2F3*48 + 5
d = 16 + 5
d = 21 dimes
and
q = 1%2F4*48 - 1
q = 12 - 1
q = 11 quarters
:
:
Check this: 48 + 21 + 11 = 80





how many coins of each kind does she have?