peer has $4.20 in dimes and quarters. He has 21 coins. How many coins of each kind does he have?
n = number of dimes
21 - n = number of quarters
.10n = value of dimes
.25(21 - n) = value of quarters
.10n + .25(21 - n) = 4.20
Solve for n, number of dimes
21 - n = number of quarters
To solve this problem, we can set up a system of equations. Let's define two variables:
- Let "D" represent the number of dimes.
- Let "Q" represent the number of quarters.
Based on the given information, we have the following equations:
1) The total value of dimes and quarters is $4.20: 0.10D + 0.25Q = 4.20.
2) The total number of coins is 21: D + Q = 21.
Now, we need to solve this system of equations. There are multiple ways to solve it, but let's solve it using the substitution method.
We can rearrange equation 2) and express D in terms of Q: D = 21 - Q.
Substitute this value of D into equation 1):
0.10(21 - Q) + 0.25Q = 4.20.
Now we simplify the equation:
2.10 - 0.10Q + 0.25Q = 4.20.
0.15Q = 2.10.
Q = 2.10 / 0.15.
Q = 14.
Now, we substitute Q = 14 back into equation 2) to find D:
D + 14 = 21.
D = 21 - 14.
D = 7.
Therefore, Peer has 7 dimes and 14 quarters.