SOLUTION: Betty found a number of nickels,dimes and quarters in her room. She found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was $11.
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-> SOLUTION: Betty found a number of nickels,dimes and quarters in her room. She found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was $11.
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Question 206016: Betty found a number of nickels,dimes and quarters in her room. She found 6 more dimes than nickels but three times as many quarters as dimes. The total value of the coins was $11.40. How many coins of each type did Betty find? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Betty found a number of nickels,dimes and quarters in her room.
She found 6 more dimes than nickels but three times as many quarters as dimes.
The total value of the coins was $11.40.
How many coins of each type did Betty find?
:
let n, d, q = no. of nickels, dimes and quarters respectively
:
Write an equation for the statements:
"6 more dimes than nickels"
d = n + 6
or
n = (d-6)
:
" three times as many quarters as dimes."
q = 3d
;
"The total value of the coins was $11.40."
.05n + .10d + .25q = 11.40
:
Substitute for n and q
.05(d-6) + .10d + .25(3d) = 11.40
:
.05d - .30 + .10d + .75d = 11.40
:
.90d = 11.40 + .30
:
.9d = 11.70
d =
d = 13 dimes
:
How many coins of each type did Betty find?
:
Use the above equations
:
n = 13 - 6
n = 7 nickels
;
q = 3(13)
q = 39 quarters
:
:
Check solution
.05(7) + .10(13) + .25(39) =
.35 + 1.30 + 9.75 = 11.40; confirms our solutions
