SOLUTION: Rita has a collection of 105 coins consisting of nickels, dimes, and quarters. The number of dimes is 5 more than one-third the number of nickels, and the number of quarters is twi
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: Rita has a collection of 105 coins consisting of nickels, dimes, and quarters. The number of dimes is 5 more than one-third the number of nickels, and the number of quarters is twice the number of dimes. how many coins of each kind does she have????
I would like help I don't know how to start.
This question is from textbook
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Rita has a collection of 105 coins consisting of nickels, dimes, and quarters. The number of dimes is 5 more than one-third the number of nickels, and the number of quarters is twice the number of dimes. how many coins of each kind does she have????
.
Let x = number of nickels
then
from:"number of dimes is 5 more than one-third the number of nickels"
(1/3)x + 5 = number of dimes
x/3 + 5 = number of dimes
from:"number of quarters is twice the number of dimes"
2((1/3)x + 5) = number of quarters
2x/3 + 10 = number of quarters
.
Our equation comes from the fact that there are 105 total coins:
x + (x/3 + 5) + (2x/3 + 10) = 105
Now, we solve for 'x'. Start by multiplying both sides by 3:
3x + x + 15 + 2x + 30 = 315
6x + 45 = 315
6x = 270
x = 45 (number of nickels)
.
dimes:
x/3 + 5 = 45/3 + 5 = 15 + 5 = 20 (number of dimes)
.
quarters:
2x/3 + 10 = 2(45)/3 + 10 = 90/3 + 10 = 30 + 10 = 40 (number of quarters)
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