Question

read the following prompt. identify the important information and then write, solve and check the equation that represents the situation.
jill sold half of her comic books and then bought sixteen more. she now has 36. how many did she begin with?
important info:

equation:

check:

Explanation:

Important Info:

• Jill sold half of her comic books.
• Then she bought 16 more.
• Now she has 36 comic books.
• We need to find the initial number of comic books (let's call it \( x \)).

Equation:

Let the initial number of comic books be \( x \). After selling half, she has \( \frac{x}{2} \) left. Then she buys 16 more, so the equation is:

$$ \frac{x}{2} + 16 = 36 $$

Solve the Equation:

Step 1: Subtract 16 from both sides

To isolate the term with \( x \), we subtract 16 from both sides of the equation:

$$ \frac{x}{2} + 16 - 16 = 36 - 16 $$

$$ \frac{x}{2} = 20 $$

Step 2: Multiply both sides by 2

To solve for \( x \), we multiply both sides of the equation by 2:

$$ 2 \times \frac{x}{2} = 20 \times 2 $$

$$ x = 40 $$

Check:

• Initial number of comic books: 40
• Sold half: \( \frac{40}{2} = 20 \)
• Bought 16 more: \( 20 + 16 = 36 \)
• This matches the number of comic books she has now (36), so the solution is correct.

Answer:

Jill began with 40 comic books.