Write a system of equations to describe the situation; solve using any method, and fill in the blanks. The Sloan family and the Gordon family are seeing a movie together. Mr. Sloan... Write a system of equations to describe the situation; solve using any method, and fill in the blanks. The Sloan family and the Gordon family are seeing a movie together. Mr. Sloan paid $10 for 1 large popcorn and 1 large drink. Mrs. Gordon bought 3 large popcorns and 4 large drinks for $34. How much does each item cost? A large popcorn costs $ and a large drink costs $. Read more

Steps to Solve

1. Define Variables

Let's define:

• Let $p$ be the cost of a large popcorn.
• Let $d$ be the cost of a large drink.

2. Set Up the Equations

From the problem:

• The Sloan family spent $10 on 1 large popcorn and 1 large drink:

  $$ p + d = 10 $$

• The Gordon family spent $34 on 3 large popcorns and 4 large drinks:

  $$ 3p + 4d = 34 $$

3. Solve the System of Equations

We now have:

1. $p + d = 10$
2. $3p + 4d = 34$

We can use substitution or elimination. Here, let's use substitution. From the first equation, we can express $d$ in terms of $p$:

$$ d = 10 - p $$

Now substitute this expression for $d$ into the second equation:

$$ 3p + 4(10 - p) = 34 $$

4. Simplify and Solve for $p$

Now, simplify the equation:

$$ 3p + 40 - 4p = 34 $$

Combine the terms:

$$ -p + 40 = 34 $$

Subtract $40$ from both sides:

$$ -p = -6 $$

Therefore:

$$ p = 6 $$

5. Find the Cost of $d$

Now, substitute $p = 6$ back into the equation for $d$:

$$ d = 10 - p $$

$$ d = 10 - 6 = 4 $$