SOLUTION: marcela ha a collection of nickels, dimes and quarters worth $24.75. The number od dimes is 10 more than twice the number of nickels, and the number of quarters is 25 more than the
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Question 997490: marcela ha a collection of nickels, dimes and quarters worth $24.75. The number od dimes is 10 more than twice the number of nickels, and the number of quarters is 25 more than the number of dimes. How many coins of each kind does she have? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Marcela has a collection of nickels, dimes and quarters worth $24.75.
The number of dimes is 10 more than twice the number of nickels,
and the number of quarters is 25 more than the number of dimes.
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
:
" Marcela has a collection of nickels, dimes and quarters worth $24.75."
.05n + .10d + .25q = 24.75
:
" The number of dimes is 10 more than twice the number of nickels,"
d = 2n + 10
we can rearrange this to
2n = d - 10
n =
:
"the number of quarters is 25 more than the number of dimes."
q = d + 25
:
Replace n and q in the first equation using the above equations
.05 + .10d + .25(d+25) = 24.75
multiply equation by 2 to get rid of the fraction
.05(d-10) + .20d + .50(d+25) = 49.50
.05d - .5 + .20d + .50d + 12.5 = 49.50
combine like terms
.05d + .20d + .50d - .5 + 12.5 = 49.50
.75d + 12 = 49.50
.75d = 49.50 - 12
.75d = 37.50
d = 37.5/.75
d = 50 dimes
then
n =
n = 20 nickels
and
q = 50 + 25
q = 75 quarters
:
:
See if the adds up
.05(20) + .10(50) + .25(75) =
1.00 + 5.00 + 18.75 = 24.75
