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?
:
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 = {{{1/3}}}n + 5
:
" the number of quarters is one less than one-fourth the number of nickels."
q = {{{1/4}}}n - 1
:
Replace d and q from the above equations:
n + ({{{1/3}}}n + 5) + ({{{1/4}}}n - 1) = 80
:
n + {{{1/3}}}n + {{{1/4}}}n - 1 + 5 = 80
:
n + {{{1/3}}}n + {{{1/4}}}n + 4 = 80
:
n + {{{1/3}}}n + {{{1/4}}}n = 80 - 4
:
n + {{{1/3}}}n + {{{1/4}}}n = 76
Get rid of those annoying fractions multiply by 12
12n + 4n + 3n = 12(76)
19n = 912
n = {{{912/19}}}
n = 48 nickels
then
d = {{{1/3}}}*48 + 5
d = 16 + 5
d = 21 dimes
and
q = {{{1/4}}}*48 - 1
q = 12 - 1
q = 11 quarters
:
:
Check this: 48 + 21 + 11 = 80






 how many coins of each kind does she have?