Andrew has 12 coins, all dimes and nickels, and they add up to $1.00. How many nickels does he have?
d = number of dimes
n = number of nickels
d + n = 10
.10d + .05n = 1.00
Solve the first equation for n or d and substitute it into the second equation.
7 quarters 3 dimes and 3 nickels
To figure out how many nickels Andrew has, we can set up a system of equations based on the given information. Let's denote the number of dimes as "D" and the number of nickels as "N".
From the problem statement, we know that Andrew has a total of 12 coins. So we can write the equation:
D + N = 12 (Equation 1)
The value of all the coins adds up to $1.00, which can be written as 10 cents for each dime (0.10D) and 5 cents for each nickel (0.05N). So we can write another equation:
0.10D + 0.05N = 1.00 (Equation 2)
Now, we have a system of equations. We can solve this system by substitution, elimination, or any other suitable method.
Let's use the substitution method to solve the system:
1. Solve Equation 1 for D: D = 12 - N
2. Substitute this value into Equation 2: 0.10(12 - N) + 0.05N = 1.00
3. Simplify the equation: 1.20 - 0.10N + 0.05N = 1.00
4. Combine like terms: -0.05N = 1.00 - 1.20
5. Simplify further: -0.05N = -0.20
6. Divide by -0.05 to isolate N: N = -0.20 / -0.05
7. Calculate: N = 4
Therefore, Andrew has 4 nickels.