Question

Keith has p pennies, n nickels, and d dimes in his pocket. The total number of coins is 9. The expression 0.01p+0.05n+0.10d represents the value of the coins, which is equal to $0.44. He has one more dime than nickels. How many pennies does Keith have? Keith has _____ pennies.

Answer 1

he has 4 pennies

2 nickels=10 cents

3 dime=30 cents

20 cents

40 +4 pennies =44 cents

Answer 2

Keith has 4 pennies, 3 dimes and 2 nickels.

Explanation:

Let the pennies be = p

Let the nickels be = n

Let the dimes be = d

Total coins Keith has = 9

So, 1st equation form :

`p+n+d=9` ....(1)

Keith has one more dime than nickels, means
`d=n+1` .....(2)

Total value of these coins is $0.44

So, third equation forms:

`0.01p+0.05n+0.10d=0.44` .....(3)

Substituting (2) in (1)

`p+n+n+1=9`

`p+2n=8` .....(4)

Similarly substitution (2) in (3)

`0.01p+0.05n+0.10(n+1)=0.44`

`0.01p+0.05n+0.10n+0.10=0.44`

`0.01p+0.15n=0.34` ....(5)

Now multiplying (4) by 0.01 and subtracting by (5)

`0.01p+0.02n=0.08` subtracting this from (5) we get

`0.13n=0.26`

So, we get n = 2

`p+2n=8`

`p+2(2)=8`

`p+4=8`

p = 4

`p+n+d=9`

`4+2+d=9`

`6+d=9`

d = 3

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Therefore, Keith has 4 pennies, 3 dimes and 2 nickels.