SOLUTION: Mary has $5.00 in nickels, dimes, and quarters. If she has twice as many dimes as quarters and sixty-seven more nickels than dimes, how many coins of each type does she have?
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Question 486401: Mary has $5.00 in nickels, dimes, and quarters. If she has twice as many dimes as quarters and sixty-seven more nickels than dimes, how many coins of each type does she have?
quarters
dimes
nickels
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Mary has $5.00 in nickels, dimes, and quarters.
If she has twice as many dimes as quarters and sixty-seven more nickels than dimes, how many coins of each type does she have?
:
Let: n = no. of nickels; d = no.of dimes; q = no of quarters
:
Write an equation for each statement:
:
"Mary has $5.00 in nickels, dimes, and quarters."
.05n + .10d + .25q = 5.00
:
"she has twice as many dimes as quarters"
d = 2q
divide both sides by 2
q = .5d
:
" sixty-seven more nickels than dimes,"
n = (d+67)
:
.05n + .10d + .25q = 5.00
Replace q with .5d, replace n with (d+67)
.05(d+67) + .10d + .25(.5) = 5.00
:
.05d + 3.35 + .10d + .125d = 5.00
:
.05d + .10d + .125d = 5.00 - 3.35
:
.275d = 1.65
d =
d = 6 dimes
:
I'll let you find the nickels and quarters, check your solutions in the 1st equation.
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