Question

Sally and Anne went to the movies. They each purchased a drink. They also bought one popcorn and one veggie cup to share. Each woman’ total is modeled with this expression:

9 + 1.34 +
1
2
(3.50 +1.74)

How would you simplify the expression? Explain your steps.

Answer 1

To simplify the expression \( 9 + 1.34 + \frac{1}{2} (3.50 + 1.74) \), we can follow these steps:

### Step 1: Simplify the parentheses
Start by simplifying the expression inside the parentheses:

\[
3.50 + 1.74 = 5.24
\]

### Step 2: Substitute back into the expression
Now substitute \( 5.24 \) back into the original expression:

\[
9 + 1.34 + \frac{1}{2} (5.24)
\]

### Step 3: Calculate the half of the sum
Next, calculate \( \frac{1}{2} \times 5.24 \):

\[
\frac{1}{2} \times 5.24 = 2.62
\]

### Step 4: Substitute again
Now substitute \( 2.62 \) back into the expression:

\[
9 + 1.34 + 2.62
\]

### Step 5: Add all the terms
Now, add all the terms together:

1. First add \( 9 + 1.34 \):

\[
9 + 1.34 = 10.34
\]

2. Then add \( 10.34 + 2.62 \):

\[
10.34 + 2.62 = 12.96
\]

### Conclusion
Thus, the simplified expression is:

\[
\boxed{12.96}
\]