Amanda buys lunch for a group of people. She buys each person a $4 sandwich, $1 French fries,
and drinks (d) which had no price listed. Then, she buys a cake and salad for everyone to share
that cost $10 and $8, respectively. If lunch was for 4 people, simplify the expression below
representing the total cost.
4 (4 + 1 + d) + 10 + 8
d + 27
d + 35
4 d + 35
4 d + 38

We are given the expression representing the total cost of lunch for 4 people. Let’s simplify it step by step.

The total cost is given as:

\[ 4(4 + 1 + d) + 10 + 8 \]

### Step 1: Simplify the expression inside the parentheses
The cost for each person’s lunch includes:
- A sandwich costing $4
- French fries costing $1
- Drinks costing $ d $

So, inside the parentheses, we have:
\[ 4 + 1 + d = 5 + d \]

### Step 2: Distribute the 4 to each term inside the parentheses
Now distribute the 4 across $ (5 + d) $:
\[ 4(5 + d) = 4 \times 5 + 4 \times d = 20 + 4d \]

### Step 3: Add the remaining costs
Next, add the shared costs of the cake and salad:
\[ 20 + 4d + 10 + 8 \]

### Step 4: Combine like terms
Now combine the constant terms:
\[ 20 + 10 + 8 = 38 \]

So the total expression simplifies to:
\[ 4d + 38 \]

Thus, the simplified expression for the total cost is:
\[ \boxed{4d + 38} \]

Let me know if you'd like more details or have any questions! Here are five related questions to explore this topic further:

1. What if the drinks cost $2 per person? What would be the total cost?
2. How would the expression change if there were 5 people instead of 4?
3. What happens to the total cost if the price of the cake increases by $5?
4. Can you factor the expression $ 4d + 38 $ further?
5. What would the expression look like if Amanda decided not to buy the cake?

**Tip**: Always simplify expressions inside parentheses before distributing any constants!

Amanda buys lunch for a group of people. She buys each person a $4 sandwich, $1 French fries, and drinks (d) which had no price listed. Then, she buys a cake and salad for everyone to share that cost $10 and $8, respectively. If lunch was for 4 people, simplify the expression below representing the total cost: 4(4 + 1 + d) + 10 + 8

Learn how to simplify an algebraic expression representing the total lunch cost for 4 people. This problem involves applying the distributive property and combining like terms. Suitable for students in Grades 6-8.

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