How many coins of 0.5 dollars each and 0.7 dollars each together make exactly 4.6 dollars?

Options

A. 1,6
B. 2,7
C. 3,5
D. 5,3

Answer

To solve the problem of how many coins of 0.5 dollars and 0.7 dollars together make exactly 4.6 dollars, we can follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = number of 0.5 dollar coins
- \( y \) = number of 0.7 dollar coins

### Step 2: Set Up the Equation
The total amount of money can be expressed as:
\[ 0.5x + 0.7y = 4.6 \]

### Step 3: Check Each Option
We will check each of the provided options to see which combination of \( x \) and \( y \) satisfies the equation.

#### Option 1: \( x = 1, y = 6 \)
\[ 0.5(1) + 0.7(6) = 0.5 + 4.2 = 4.7 \quad (\text{Not } 4.6) \]

#### Option 2: \( x = 2, y = 7 \)
\[ 0.5(2) + 0.7(7) = 1 + 4.9 = 5.9 \quad (\text{Not } 4.6) \]

#### Option 3: \( x = 3, y = 5 \)
\[ 0.5(3) + 0.7(5) = 1.5 + 3.5 = 5.0 \quad (\text{Not } 4.6) \]

#### Option 4: \( x = 5, y = 3 \)
\[ 0.5(5) + 0.7(3) = 2.5 + 2.1 = 4.6 \quad (\text{This is correct!}) \]

### Conclusion
The correct combination of coins is:
- 5 coins of 0.5 dollars
- 3 coins of 0.7 dollars

### Final Answer
The answer is \( (5, 3) \).

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