A girl has 12 apples more than the number of apples a boy had. The total number of apples altogether are greater than 45. Write and simplify the inequality. 

Let the number of apples the boy has be denoted as \( x \).

According to the problem, the girl has 12 more apples than the boy, so the number of apples the girl has is \( x + 12 \).

The total number of apples altogether is the sum of the boy's and girl's apples, which is:

\[
x + (x + 12) = 2x + 12
\]

We are also told that the total number of apples is greater than 45. This gives the inequality:

\[
2x + 12 > 45
\]

Now, simplify the inequality:

1. Subtract 12 from both sides:

\[
2x > 33
\]

2. Divide both sides by 2:

\[
x > 16.5
\]

Therefore, the number of apples the boy has must be greater than 16.5, which implies \( x \geq 17 \) (since \( x \) must be a whole number in this context).

### Simplified inequality:
\[
x > 16.5 \quad \text{or} \quad x \geq 17 \quad (\text{if we assume whole numbers})
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. If the boy had 18 apples, how many apples does the girl have?
2. What happens if the total number of apples is exactly 45?
3. Can the boy have a fractional number of apples? Why or why not?
4. How would the inequality change if the total apples were less than 50?
5. What if the girl had 10 apples more than the boy?

**Tip:** Always verify if whole numbers are expected in real-world scenarios, especially when dealing with objects like apples!

A girl has 12 apples more than the number of apples a boy had. The total number of apples altogether are greater than 45. Write and simplify the inequality.

Learn how to solve a word problem involving an inequality where a girl has 12 more apples than a boy, and the total number of apples is greater than 45. This problem introduces algebraic concepts and simplifying inequalities, suitable for students in Grades 6-8.

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