Respuesta :
Answer:
$6.22
Step-by-step 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
Answer:
The bag contains 7 pennies, 16 dimes, 11 nickels and 16 quarters and a total of $6.22
Step-by-step explanation:
Given
[tex]Coins = 50[/tex]
[tex]Pennies = 14%[/tex]%
[tex]Dimes = 32%[/tex]%
Nickel = 4 more than pennies
Required
How much money does the bag contain?
We start by calculating the number of pennies
[tex]Pennies = 14%[/tex]% of total
So,
[tex]Pennies = \frac{14}{100} * 50[/tex]
[tex]Pennies = \frac{14 * 50}{100}[/tex]
[tex]Pennies = \frac{700}{100}[/tex]
[tex]Pennies = 7[/tex]
Also, [tex]Dimes = 32%[/tex]% of total
[tex]Dimes = \frac{32}{100} * 50[/tex]
[tex]Dimes = \frac{1600}{100}[/tex]
[tex]Dimes = 16[/tex]
The question says there are 4 more nickels than pennies;
This means
[tex]Nickels = 4 + Pennies[/tex]
Recall that [tex]Pennies = 7[/tex]
So,
[tex]Nickels = 4 + 7[/tex]
[tex]Nickels = 11[/tex]
The question also says that the bag contains quarters;
If total coins is 50, then
[tex]Quarters = Total - Nickels - Dimes - Pennies[/tex]
[tex]Quarters = 50 - 11 - 16 - 7[/tex]
[tex]Quarters = 16[/tex]
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
