Answer:
Gaby has 27 dimes in her piggy bank.
Gaby has 44 nickels in her piggy bank.
Explanation:
We can use a system of equations to determine the number of nickels and dimes Gaby has, where:
- N represents the number of nickels,
- and D represents the number of dimes.
First equation:
We know that the sum of the worth of the nickels ($0.05 * quantity) and dimes ($0.10 * quantity) equals the total worth of 4.90:
(0.05 * quantity) + (0.10 * quantity) = 4.90
Thus, our first equation is given by:
0.05N + 0.10D = 4.90
Second equation:
- We also know that the sum of the nickels and dimes equals 71.
Thus, our second equation is given by:
N + D = 71
Method to solve: Substitution:
First, we can isolate N in the second equation:
(N + D = 71) - D
N = -D + 71
Solving for D (the number of dimes):
Now we can substitute -D + 71 for N in the first equation to solve for D (the number of dimes):
0.05(-D + 71) + 0.10D = 4.90
-0.05D + 3.55 + 0.10D = 4.90
(0.05D + 3.55 = 4.90) - 3.55
(0.05D = 1.35) / 0.05
D = 27
Thus, Gaby has 27 dimes in her piggy bank.
Solving for N (the number of nickels):
Now we can solve for N by plugging in 27 for D in the second equation:
(N + 27 = 71) - 27
N = 44
Thus, Gaby has 44 nickels in her piggy bank.