(a)

Question

Part A
Sammie spent half of her money at the mall this weekend. Her uncle gave for $50 extra for school supplies. Write an equation to determine how much money Sammie had if she came home $90.

A
50
x
+
2
1
=90

B
50
x
+90=
2
1


C
2
1
x−50=90

D
2
1
x+50=90

(b)


Part B

Using the information in PART A, how much money did Sammie have when she went to the mall?

$

Answer 1

Let's analyze Part A first. We know the following:

• Let \( x \) represent the amount of money Sammie had before going to the mall.
• She spent half of her money at the mall, which means she spent \( \frac{1}{2}x \).
• After spending that money, she received $50 from her uncle.
• She came home with $90.

Putting this together, we can write the equation based on her situation:

1. After spending half of her money, she had \( x - \frac{1}{2}x = \frac{1}{2}x \).
2. Then, she received $50, so the amount she came home with is \( \frac{1}{2}x + 50 \).
3. This amount equals $90.

So we can write the equation:

\[ \frac{1}{2}x + 50 = 90 \]

Thus, the correct equation from the options you provided is:

D: \( \frac{1}{2} x + 50 = 90 \)

---

Now, let's solve Part B to determine how much money Sammie had when she went to the mall.

From the equation we found in Part A:

\[ \frac{1}{2}x + 50 = 90 \]

To isolate \( x \), first subtract 50 from both sides:

\[ \frac{1}{2}x = 90 - 50 \] \[ \frac{1}{2}x = 40 \]

Next, multiply both sides by 2 to solve for \( x \):

\[ x = 40 \times 2 \] \[ x = 80 \]

Therefore, Sammie had $80 when she went to the mall.