1. Problem: You saw a group of sheep with a total of 28 legs and 14 eyes. How many sheep are there?
- Each sheep has 4 legs and 2 eyes.
- Let the number of sheep be $x$.
- Total legs: $4x = 28$.
- Total eyes: $2x = 14$.
2. Solve for $x$ using legs:
$$4x = 28$$
$$x = \frac{28}{4} = 7$$
3. Check with eyes:
$$2x = 14$$
$$x = \frac{14}{2} = 7$$
4. Both match, so the number of sheep is $7$.
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5. Problem: Given the height relations:
- Abdullah is taller than Mohammad.
- Mohammad is shorter than Khalid and taller than Mahmoud.
Who is the shortest?
6. From the relations:
- $A > M$
- $K > M > Ma$
7. Ordering from tallest to shortest:
$$K > A > M > Ma$$
8. The shortest is Mahmoud.
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9. Problem: Find the 999th term of the sequence $55, 60, 65, \ldots$
10. This is an arithmetic sequence with first term $a_1 = 55$ and common difference $d = 5$.
11. The $n$th term formula:
$$a_n = a_1 + (n-1)d$$
12. Substitute $n=999$:
$$a_{999} = 55 + (999-1) \times 5 = 55 + 998 \times 5 = 55 + 4990 = 5045$$
13. The 999th term is $5045$.
Final answers:
- Number of sheep: 7
- Shortest person: Mahmoud
- 999th term: 5045
Sheep Height Sequence
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