SOLUTION: Solve the problem: Joe has a collection of nickels and dimes that is worth $6.00. If the number of dimes was doubled and the number of nickels was increased by 6, the value of the
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Question 187524: Solve the problem: Joe has a collection of nickels and dimes that is worth $6.00. If the number of dimes was doubled and the number of nickels was increased by 6, the value of the coins would be $9.90.
How many dimes does he have?
You can put this solution on YOUR website! oe has a collection of nickels and dimes that is worth $6.00.
If the number of dimes was doubled and the number of nickels was increased by 6,
the value of the coins would be $9.90.
How many dimes does he have?
:
Let n = no. of nickels; Let d = no. of dimes (originally)
:
"a collection of nickels and dimes that is worth $6.00."
.05n + .10d = 6.00
or
.05n = 6.00 - .10d
n = - d
n = 120 - 2d
:
"If the number of dimes was doubled and the number of nickels was increased by 6, the value of the coins would be $9.90."
.05(n+6) + 2(.10d) = 9.90
.05n + .3 + .20d = 9.90
.05n + .20d = 9.90 - .3
.05n + .20d = 9.60
:
Substitute (120-2d) for n in the above equation:
.05(120-2d) + .20d = 9.60
6 - .10d + .20d = 9.60
-.10d + .20d = 9.60 - 6
.10d = 3.60
d =
d = 36 dimes
:
:
Find the no. of nickels to check our solution
n = 120 - 2d
n = 120 - 2(36)
n = 120 - 72
n = 48 nickels
;
.05(48) + .10(36) =
2.40 + 3.60 = 6.00; confirms our solution
