Evan has $0.45 worth of pennies and nickels. He has a total of 21 pennies and nickels altogether. Determine the number of pennies and the number of nickels that Evan has.

What should be done is to propose a system of equations that includes in one equation the total number of coins and the other with the total value of the coins. With quantity of Pennies (P) and quantity of Nickels (N), we have to:

P + N = 21, reorganizing

P = 21 - N (1)

Let $ 0.45 = 45 cents. Now, knowing that Pennies (P) are 1 cent and nickels (N) 5 cents we have to:

P + 5 * N = 45 (2)

Replacing (1) in (2):

21 - N + 5 * N = 45, solving

4 * N = 45-21

N = 24/4 = 6

And now to replace this in (1)

P = 21 - 6

P = 15

Checking with equation (2)

15 + 5 * 6 = 45

Therefore there are 15 Pennies and 6 Nickels

adioabiola adioabiola · Answer 2 · 2021-12-10T09:07:29+01:00

The number of pennies and nickels that has a worth of $0.45 is 15 and 6 respectively

Given:

total worth = $0.45

Total coins = 21

let

number of pennies = x

number of nickels = y

x + y = 21 (1)

0.01x + 0.05y = 0.45 (2)

multiply (1) by 0.01

0.01x + 0.01y = 0.21 (3)

0.01x + 0.05y = 0.45 (2)

subtract (2) from (1)

0.05y - 0.01y = 0.45 - 0.21

0.04y = 0.24

y = 0.24 / 0.04

y = 6

substitute y = 6 into (1)

x + y = 21 (1)

x + 6 = 21

x = 21 - 6

x = 15

Therefore, the number of pennies and nickels that has a worth of $0.45 is 15 and 6 respectively.

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