a. The system of equations that represents this scenario is : D + n = 29 and 0.1D + 0.05n = 2.15.
b. The numbers of nickels and dimes are 15 and 14, respectively.
We have a total of 29 coins in our piggy bank. All the coins are either nickels or dimes. The value of the coins is $2.15. We have to find out the equation that represents this scenario. We have to find out the number of nickels and dimes that we have in the piggy bank.
Let the number of dimes and nickels be represented by the variables "D" and "n", respectively. The value of a dime is $0.1. The value of a nickel is $0.05. The equations are given below.
D + n = 29
0.1D + 0.05n = 2.15
We will substitute the value of "D" from the first equation into the second equation.
D = 29 - n
0.1D + 0.05n = 2.15
0.1(29 - n) + 0.05n = 2.15
2.9 - 0.1n + 0.05n = 2.15
0.05n = 0.75
n = 15
Hence, the number of nickels is 15. We will substitute this value into the first equation.
D = 29 - n
D = 29 - 15
D = 14
Hence, the number of dimes is 14.
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