A bank teller knows she received 34 dimes and nickels combined from a customer. If the change totaled $2.05 how many nickels and dimes did she receive.
25 nickels and 9 dimes
To solve this problem, we can set up a system of equations. Let's use the variables "d" to represent the number of dimes and "n" to represent the number of nickels.
The first equation represents the total number of coins: d + n = 34.
The second equation represents the total value of the coins: 0.10d + 0.05n = 2.05.
Now we can solve this system of equations.
1. Start by isolating one of the variables in either equation. Let's solve the first equation for d: d = 34 - n.
2. Substitute this expression for d in the second equation:
0.10(34 - n) + 0.05n = 2.05.
3. Distribute and simplify:
3.4 - 0.10n + 0.05n = 2.05.
4. Combine like terms:
-0.05n = 2.05 - 3.4,
-0.05n = -1.35.
5. Divide both sides of the equation by -0.05 to solve for n:
n = (-1.35) / (-0.05),
n = 27.
Now that we have found n, we can substitute this value back into the first equation to find d:
d = 34 - n,
d = 34 - 27,
d = 7.
Therefore, the bank teller received 7 dimes and 27 nickels.
n+d = 34
5n+10d = 205
now solve as usual