Answer:
Option D is correct.
There are 34 nickels in the piggy bank.
Step-by-step explanation:
A piggy bank contains pennies, nickels and dimes.
Let the number of pennies be p
Let the number of nickels be n
Let the number of dimes be d
Also, note that 1 penny = $0.01
1 nickel = $0.05
1 dime = $0.10
- The number of dimes is 15 more than the number of nickels.
d = 15 + n
- There are 140 coins altogether totaling $7.17.
p + n + d = 140
0.01p + 0.05n + 0.1d = 7.17
Bringing the 3 equations together
d = 15 + n (eqn 1)
p + n + d = 140 (eqn 2)
0.01p + 0.05n + 0.1d = 7.17 (eqn 3)
Substitute (eqn 1) into (eqn 2)
p + n + d = 140
p + n + (15 + n) = 140
p + 2n + 15 = 140
p = 140 - 15 - 2n = 125 - 2n
p = 125 - 2n (eqn 4)
Substitute (eqn 1) and (eqn 4) into (eqn 3)
0.01p + 0.05n + 0.1d = 7.17
0.01(125 - 2n) + 0.05n + 0.1(15 + n) = 71.7
1.25 - 0.02n + 0.05n + 1.5 + 0.1n = 7.17
0.1n + 0.05n - 0.02n + 1.5 + 1.25 = 7.17
0.13n + 2.75 = 7.17
0.13n = 7.17 - 2.75 = 4.42
0.13n = 4.42
n = (4.42/0.13) = 34
d = 15 + n = 15 + 34 = 49
p = 125 -2n = 125 - (2×34) = 125 - 68 = 57
Hence, there are 57 pennies, 34 nickels and 49 dimes in the piggy bank.
Hope this Helps!!!
