Question

emily was going to sell all of her stamp collection to buy a video game. after selling half of them she changed her mind. she then bought seventeen more. write an expression for how many she has now. a. $17 - \frac{1}{2}s$ b. $s - \frac{1}{2} + 17$ c. $s + 17$ d. $\frac{1}{2}s + 17$ reset selection

Explanation:

Step1: Define the variable

Let \( s \) be the number of stamps Emily originally had.

Step2: Calculate the number after selling half

After selling half of her stamps, the number of stamps she has left is \( \frac{1}{2}s \) (since half of \( s \) is \( \frac{1}{2}s \)). Wait, no, actually, if she sells half, she has \( s-\frac{1}{2}s=\frac{1}{2}s \) left? Wait, no, let's re - think. If she has \( s \) stamps and sells half, the number she has left is \( s-\frac{1}{2}s=\frac{1}{2}s \)? Wait, no, that's not right. Wait, if you have \( s \) items and you sell half, the number remaining is \( s-\frac{1}{2}s=\frac{1}{2}s \)? Wait, no, actually, the number remaining is \( s - \frac{1}{2}s=\frac{1}{2}s \)? Wait, no, let's take an example. If \( s = 10 \), selling half (5) means she has \( 10 - 5=5=\frac{1}{2}\times10 \). So after selling half, she has \( \frac{1}{2}s \) stamps left.

Step3: Calculate the number after buying 17 more

Then she buys 17 more. So the number of stamps she has now is the number she had after selling half plus 17. So that is \( \frac{1}{2}s+17 \).

Wait, let's check the options. Option D is \( \frac{1}{2}s + 17 \). Let's analyze the other options:

• Option A: \( 17-\frac{1}{2}s \) implies she has 17 minus half of her original stamps, which doesn't make sense because she started with \( s \) stamps and sold half, then bought 17.
• Option B: \( s-\frac{1}{2}+17 \) is incorrect because \( \frac{1}{2} \) without multiplying by \( s \) is wrong. It should be \( \frac{1}{2}s \) not \( \frac{1}{2} \).
• Option C: \( s + 17 \) ignores the fact that she sold half of her stamps.

Answer:

D. \(\frac{1}{2}s + 17\)