SOLUTION: I have some change (pennies, nickels, and dimes) in my pocket. Fourteen of the coins are dimes, 25% of them are nickels, and five-ninths of them are pennies. What is the total valu

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Question 620589: I have some change (pennies, nickels, and dimes) in my pocket. Fourteen of the coins are dimes, 25% of them are nickels, and five-ninths of them are pennies. What is the total value of my change?
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
I have some change (pennies, nickels, and dimes) in my pocket.
Fourteen of the coins are dimes, 25% of them are nickels, and five-ninths of them are pennies.
What is the total value of my change?
:
Let p = no. of pennies
Let n = no. of nickels
no. of dimes given as 14
Let t = total number of coins
:
Find the total number coins first
:
"25% of them are nickels,"
n = 1%2F4t
:
"five-ninths of them are pennies."
p = 5%2F9t
:
t = p + n + 14
Replace p and n
t = 5%2F9t + 1%2F4t + 14
multiply by 36 to clear the denominators, results
36t = 4(5t) + 9t + 36(14)
36t = 20t + 9t + 504
36t = 29t + 504
36t - 29t = 502
7t = 504
t = 504/7
t = 72 coins
then
p = 5%2F9(72)
p = 40 pennies
and
n = 1%2F4(72)
n = 18 nickels
:
" What is the total value of my change?"
V = .01(40) + .05(18) + .10(14)
V = .40 + .90 + 1.40
V = $2.70

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

I have some change (pennies, nickels, and dimes) in my pocket. Fourteen of the coins are dimes, 25% of them are nickels, and five-ninths of them are pennies. What is the total value of my change?

Let total amount of coins be A

¼ of coins are nickels

5%2F9 of coins are pennies

Therefore, fraction of coins that are dimes = 1+-+%281%2F4+%2B+5%2F9%29%29, or 1+-+29%2F36, or 7%2F36

Now, since amount of dimes = 14, then we can say that: 7%2F36+=+14, and also that: %287%2F36%29%2F1+=+14%2FA

A%287%2F36%29+=+14 ----- Cross-multiplying

7A%2F36+=+14

7A = 504 ------ Cross-multiplying

A, or total amount of coins = 504%2F7, or 72

14 dimes = $1.40

Amount of nickels = 1%2F4 of 72, or 18, for a value of $0.90

Amount of pennies = 5%2F9 of 72, or 40, for a value of $0.40

Total value of change = $1.40 + 0.90 + 0.40 = $highlight_green%282.70%29

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