How Many of Each Coin Do I Have If I Have $1.60 in Total, Some Are Quarters and Some Are Dimes, and I Have 10 Coins Total?

If you have a total of $1.60 consisting of quarters and dimes, and you have 10 coins in total, you can determine the number of each type of coin using a simple system of equations.

Let’s denote:

• q as the number of quarters
• d as the number of dimes

We know the following:

1. The total number of coins is 10: q + d = 10
2. The total value of the coins is $1.60: 0.25q + 0.10d = 1.60

To solve this system of equations, follow these steps:

1. From the first equation, express d in terms of q: d = 10 – q
2. Substitute this expression into the second equation: 0.25q + 0.10(10 – q) = 1.60
3. Simplify the equation: 0.25q + 1 – 0.10q = 1.60
4. Combine like terms: 0.15q + 1 = 1.60
5. Subtract 1 from both sides: 0.15q = 0.60
6. Divide both sides by 0.15: q = 4
7. Substitute q = 4 back into the first equation to find d: d = 10 – 4 = 6

So, you have 4 quarters and 6 dimes.

This means you have 4 quarters (which total $1.00) and 6 dimes (which total $0.60), adding up to $1.60 with 10 coins in total.