Jennifer sells photos. After selling half her photos she stopped selling them and then bought 4 more. Now she has 26. How many did she start with?
The correct answer and explanation is:
Let the number of photos Jennifer initially had be xx.
- First, she sells half of her photos. After selling, she has x2\frac{x}{2} photos left.
- Then, she buys 4 more photos, so now she has x2+4\frac{x}{2} + 4 photos.
- According to the problem, after buying 4 more photos, she has 26 photos in total.
Therefore, we can write the equation: x2+4=26\frac{x}{2} + 4 = 26
- Subtract 4 from both sides to isolate x2\frac{x}{2}:
x2=22\frac{x}{2} = 22
- Multiply both sides by 2 to solve for xx:
x=44x = 44
Thus, Jennifer started with 44 photos.
Explanation:
This is a straightforward problem involving basic algebra. The key steps involve translating the story into a mathematical equation and solving it step by step. First, the fact that she sold half her photos and then bought 4 more forms the basis of the equation. By subtracting the number of photos she bought (4), we find the number of photos she had after selling half of them. This leads us to the equation x2+4=26\frac{x}{2} + 4 = 26, and solving this gives us the original number of photos she had, which is 44.
The core of the solution involves setting up the equation correctly and applying algebraic operations such as multiplication and subtraction to isolate and solve for xx. This approach works for many similar word problems that involve changes in quantities.