John and 4 friends are going out for pizza for lunch. They split one pizza and 5 large drinks. The pizza cost $10.00. After using a $4.00 gift certificate, they spend a total of $13.50. Write an equation to model this situation, and find the cost of one large drink.

Answer 1

Let's break down the problem and set up an equation to model the situation.

First, let's define the variables and the known quantities:
- Cost of one large drink: \( d \)
- Total cost of the pizza and drinks: \( 10.00 + 5d \)
- Amount of the gift certificate: \( 4.00 \)
- Total amount spent after the gift certificate: \( 13.50 \)

To find the total spending after using the gift certificate, we subtract the value of the gift certificate from the total cost of the pizza and drinks:
\[
(10.00 + 5d) - 4.00 = 13.50
\]

Now we solve for \( d \):
\[
10.00 + 5d - 4.00 = 13.50
\]

Simplify the left side of the equation:
\[
6.00 + 5d = 13.50
\]

Subtract 6.00 from both sides to isolate the term with \( d \):
\[
5d = 7.50
\]

Divide both sides by 5 to solve for \( d \):
\[
d = \frac{7.50}{5} = 1.50
\]

So, the cost of one large drink is \( 1.50 \).

To ensure the calculation is correct, we can verify by plugging \( d = 1.50 \) back into the total cost equation:
\[
10.00 + 5(1.50) - 4.00 = 13.50
\]
\[
10.00 + 7.50 - 4.00 = 13.50
\]
\[
17.50 - 4.00 = 13.50
\]
\[
13.50 = 13.50
\]

The verification confirms the solution is correct. Thus, the cost of one large drink is \( \boxed{1.50} \).