Question

A bad contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 14% are pennies are 32% are dimes. There are 4 more nickels than pennies. How much money does the bag contain?

Answer 1

The bag contains 7 pennies, 16 dimes, 11 nickels and 16 quarters and a total of $6.22

Explanation:

Given

`Coins = 50`

`Pennies = 14%`%

`Dimes = 32%`%

Nickel = 4 more than pennies

Required

How much money does the bag contain?

We start by calculating the number of pennies

`Pennies = 14%`% of total

So,

`Pennies = (14)/(100) * 50`

`Pennies = (14 * 50)/(100)`

`Pennies = (700)/(100)`

`Pennies = 7`

Also,
`Dimes = 32%`% of total

`Dimes = (32)/(100) * 50`

`Dimes = (1600)/(100)`

`Dimes = 16`

The question says there are 4 more nickels than pennies;

This means

`Nickels = 4 + Pennies`

Recall that
`Pennies = 7`

So,

`Nickels = 4 + 7`

`Nickels = 11`

The question also says that the bag contains quarters;

If total coins is 50, then

`Quarters = Total - Nickels - Dimes - Pennies`

`Quarters = 50 - 11 - 16 - 7`

`Quarters = 16`

Converting each of these to dollars

1 penny = $0.01

7 pennies = 7 * $0.01 = $0.07

1 nickel = $0.05

11 nickels = 11 * $0.05 = $0.55

1 dime = $0.10

16 dimes = $0.10 * 16 = $1.6

1 quarter = $0.25

16 quarters = $0.25 * 16 = $4

Total = $0.07 + $0.55 + $1.6 + $4

Total = $6.22

Hence, the bag contains 7 pennies, 16 dimes, 11 nickels and 16 quarters and a total of $6.22

Answer 2

$6.22

Explanation:

Given;

Total number of coins N = 50

Number of pennies p = 14% of N = 0.14 × 50 = 7

Number of dimes d = 32% of N = 0.32×50 = 16

Number of nickels n = 4 + number of pennies = 4+p

n = 4+7 = 11

Number of quarters q;

N = p+d+n+q

q = N - (p+d+n)

q = 50-(7+16+11)

q = 16

1 Penny = 1 cent = $0.01

1 Nickel = 5 cent = $0.05

1 dime = 10 cents = $0.10

1 quarter = 25 cents = $0.25

Total amount in the bag is;

C = 0.01p + 0.05n + 0.10d +0.25q

Substituting the values;

C = 0.01(7) + 0.05(11) + 0.10(16) + 0.25(16)

C = $6.22

The bag contains $6.22