Simplify the following`:`
`43.16+493.28-507.34`

Options

A. 29.5
B. 29.1
C. 417.54
D. 143.78

Answer

To simplify the expression \( 43.16 + 493.28 - 507.34 \), we will follow these steps:

### Step 1: Add the first two numbers
We start by adding \( 43.16 \) and \( 493.28 \).

\[ \begin{array}{r} 43.16 \\ + 493.28 \\ \hline \end{array} \]

Align the numbers by the decimal point and add:

- **Hundredths place**: \( 6 + 8 = 14 \) (write down 4 and carry over 1)
- **Tenths place**: \( 1 + 2 + 1 = 4 \) (including the carry)
- **Units place**: \( 3 + 3 = 6 \)
- **Tens place**: \( 4 + 9 = 13 \) (write down 3 and carry over 1)
- **Hundreds place**: \( 1 \) (from carry)

So, \( 43.16 + 493.28 = 536.44 \).

### Step 2: Subtract the third number
Now, we subtract \( 507.34 \) from \( 536.44 \).

\[ \begin{array}{r} 536.44 \\ - 507.34 \\ \hline \end{array} \]

Align the numbers by the decimal point and subtract:

- **Hundredths place**: \( 4 - 4 = 0 \)
- **Tenths place**: \( 4 - 3 = 1 \)
- **Units place**: \( 6 - 7 \) (we need to borrow from the tens place, making it \( 16 - 7 = 9 \))
- **Tens place**: After borrowing, \( 2 - 0 = 2 \)
- **Hundreds place**: \( 5 - 5 = 0 \)

So, \( 536.44 - 507.34 = 29.10 \).

### Final Answer
Thus, the simplified result is:

\[ \boxed{29.10} \]