17. Higher Order Thinking A store sells 3 pens in a package. There are 12 packages of pens in a box. Write an equation to model the number of pens in a box. Use the equation to write another equation that uses the Subtraction Property of Equality. Explain how the equation is balanced.

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To solve the problem, let's break it down step by step.

### Step 1: Extract Known Conditions
- Each package contains 3 pens.
- There are 12 packages in a box.

### Step 2: Write an Equation to Model the Number of Pens in a Box
Let $$ p $$ represent the total number of pens in a box. The equation can be modeled as:
$$
p = 3 \times 12
$$

### Step 3: Calculate the Total Number of Pens
Now, let's calculate the total number of pens in the box:
$$
p = 3 \times 12 = 36
$$
So, there are 36 pens in a box.

### Step 4: Write Another Equation Using the Subtraction Property of Equality
The Subtraction Property of Equality states that if you subtract the same number from both sides of an equation, the two sides remain equal.

We can create a new equation by subtracting a certain number of pens from both sides. Let's say we subtract 6 pens from the total number of pens in the box:
$$
p - 6 = 36 - 6
$$
This simplifies to:
$$
p - 6 = 30
$$

### Step 5: Explain How the Equation is Balanced
In the equation $$ p - 6 = 30 $$, we started with the original equation $$ p = 36 $$. By subtracting 6 from both sides, we maintain the equality because we are performing the same operation on both sides of the equation.

Thus, if $$ p $$ originally equals 36, subtracting 6 from both sides gives us:
- Left side: $$ 36 - 6 = 30 $$
- Right side: $$ p - 6 $$

Both sides are equal to 30, demonstrating that the equation is balanced.

### Summary
1. The equation modeling the number of pens in a box is $$ p = 3 \times 12 $$.
2. The equation using the Subtraction Property of Equality is $$ p - 6 = 30 $$.
3. The equation is balanced because the same value (6) was subtracted from both sides, keeping the equality intact.
There are 36 pens in a box. If you subtract 6 pens, the equation becomes $$ p - 6 = 30 $$. The equation remains balanced because the same number is subtracted from both sides.

17. Higher Order Thinking A store sells 3 pens in a package. There are 12 packages of pens in a box. Write an equation to model the number of pens in a box. Use the equation to write another equation that uses the Subtraction Property of Equality. Explain how the equation is balanced.

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