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Kent has a collection of pennies and nickels with a value of 1.98$. the number of pennies he has is five less than twice the number of nickels. how many of each coin does Kent have?
1 define your variables ,- what are you solving for
2 set up equations - using the information given
3 solve the system using your method of choice

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Answer with Step-by-step explanation:

We are given that:

  • Kent has a collection of pennies and nickels with a value of 1.98$.
  • The number of pennies he has is five less than twice the number of nickels.  

1. Let p be the number of pennies

and n be the number of nickles

2. Then, p=2n-5

1 pennie=$0.01

1 nickle=$0.05

0.01p+0.05n=1.98

Multiplying both sides by 100,we get

p+5n=198

3. Putting p=2n-5 in p+5n=198,we get

2n-5+5n=198

7n=198+5

7n=203

n=29

Putting value of n in p=2n-5, we get

p=2×29-5

p= 58-5

p= 53

Hence, Number of pennies=53

and number of nickle=29

Kent has 53 Pennies and 29 Nickels in his collection.

    Let the number of pennies with Kent = P

    And the number of nickels = N

Therefore, value of pennies = $0.01P

And the value of nickels = $0.05N

It's given that the "value of pennies and nickels" in the collection = $1.98

Therefore, equation for the value will be,

0.01P + 0.05N = 1.98

P + 5N = 198 -------(1)

 "Number of pennies is five less than twice the number of nickels"

Therefore, equation will be,

P = 2N - 5

2N - P = 5 --------(2)

By adding equations (1) and (2),

(P + 5N) + (2N - P) = 198 + 5

7N = 203

N = 29

By substituting the value of N in equation (1),

P + 5(29) = 198

P = 198 - 145

P = 53

   Therefore, Kent has 53 Pennies and 29 Nickels in his collection.

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