Question

One- & Two-Step Equations Unit Test
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Question
Reann has stickers. She gives her friend half, and then her brother gives her 8 new ones. She ends up with 12 stickers. How many did she start with? Identify the operations needed to solve this problem.(1 point)
Responses

subtraction and division
subtraction and division

subtraction and multiplication
subtraction and multiplication

addition and division
addition and division

addition and multiplication

Answer 1

Let's break down the problem step by step to identify the operations needed.

1. Let \( x \) be the number of stickers Reann started with.
2. She gives away half of her stickers, which means she gives away \( \frac{x}{2} \). Therefore, she has \( x - \frac{x}{2} = \frac{x}{2} \) stickers left after giving the half away.
3. Her brother gives her 8 new stickers, so now she has \( \frac{x}{2} + 8 \).
4. According to the problem, after this, she ends up with 12 stickers. So, we can set up the equation:

\[
\frac{x}{2} + 8 = 12
\]

Now let's solve for \( x \):

- First, subtract 8 from both sides:

\[
\frac{x}{2} = 12 - 8 \\
\frac{x}{2} = 4
\]

- Next, multiply both sides by 2:

\[
x = 4 \times 2 \\
x = 8
\]

Now, let's identify the operations:
1. We subtracted 8 to isolate the term with \( x \) (subtraction).
2. We multiplied by 2 to solve for \( x \) (multiplication).

Thus, the identified operations used to solve this problem are **subtraction and multiplication**.

So the correct answer is:
**subtraction and multiplication**.