Sure! Let's go through the steps to simplify and evaluate the given expression for the total amount that Lance and his 7 friends spent at the activity center.
1. Identify the cost components per person:
- Dinner: [tex]$\$[/tex] 5.95[tex]$
- Laser tag: $[/tex]\[tex]$ 4$[/tex]
- Bowling shoes: [tex]$\$[/tex] 3.60[tex]$
- Video games: $[/tex]\[tex]$ 2.25$[/tex]
2. Rewrite the expression:
The problem gives us the total amount spent as:
[tex]\[
8 \cdot (5.95) + 8 \cdot (4) + 8 \cdot (3.60) + 8 \cdot (2.25)
\][/tex]
Using the distributive property, we can factor out the 8 since each person pays for each activity:
[tex]\[
8 \cdot (5.95 + 4 + 3.60 + 2.25)
\][/tex]
3. Evaluate the expression inside the parentheses first:
[tex]\[
5.95 + 4 + 3.60 + 2.25
\][/tex]
Adding these costs together:
[tex]\[
5.95 + 4 = 9.95
\][/tex]
[tex]\[
9.95 + 3.60 = 13.55
\][/tex]
[tex]\[
13.55 + 2.25 = 15.80
\][/tex]
So, the total cost per person is:
[tex]\[
15.80
\][/tex]
4. Multiply this total cost per person by the number of people (8):
[tex]\[
8 \cdot 15.80
\][/tex]
Therefore, evaluating this expression gives us:
[tex]\[
8 \cdot 15.80 = 126.40
\][/tex]
So, Lance and his 7 friends spent a total of [tex]\( \boxed{126.40} \)[/tex] dollars.
