Kendyl had a piggy bank that contained only pennies and dimes. Her piggy bank contained a total of $4.12. She had a total of 178 coins. Which systems of equations below can be used to find how many pennies and dimes Kendyl has in her piggy bank? Let p represent pennies, and d represent dimes. Select the correct letter choice.
A.{p+d=$4.121p+10d=178
B.{p+d=178.01p+.10d=$4.12
C.{p+d=1781p+10d=$4.12
D.{p+10d=$4.12.01p+.10d=178
The correct answer is B.{p+d=178, 01p+.10d=$4.12.
This is because the first equation represents the total number of coins in the piggy bank, which is 178. The second equation represents the total value of the coins in dollars, which is $4.12.
Using your answer from Part A, if Kendyl has pennies and dimes in her piggy bank with a total of 178 coins, and she has $4.12 in her piggy bank, how many dimes does she have?
To find the number of dimes Kendyl has, we can solve the system of equations mentioned in Part A, which was B.{p+d=178, 01p+.10d=$4.12.
Let's rearrange the first equation to solve for p: p = 178 - d
Substituting this into the second equation: 0.01(178 - d) + 0.10d = 4.12
Expanding and solving for d:
1.78 - 0.01d + 0.10d = 4.12
0.09d = 2.34
d = 26
Therefore, Kendyl has 26 dimes in her piggy bank.