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

Answer:

Keith has 4 pennies, 3 dimes and 2 nickels.

Step-by-step 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.