Question

Signs are placed at the beginning and at the end of a 4​-kilometer hiking trail. Signs are also placed every 500 meters along the trail. How many signs are along the​ trail? Explain. Since 4 kilometers is equal to 4000 ​meters, the equation m times 500 equals 4 comma 000 can be written to find the number of signs after the beginning sign.​ Then, since mequals 7 signs after the beginning​ sign, there are a total of 8 signs on the entire trail. ​(Type whole​ numbers.)

Answer 1

9 Signs

Explanation:

The hiking trail is 4 kilometer long.

Signs are placed at the beginning and at the end of the trail.

4km = 4000m

We can solve this using simple arithmetic progression.

• The first term,a= 0
• The common difference,d= 500.
• The last term,l= 4000.

Therefore:

Last term, l=a+(n-1)d

4000=0+500(n-1)

4000=500n-500

4000+500=500n

4500=500n

Divide both sides by 500

n=9

Therefore, there are a total of 9 signs on the entire trail.

CHECK

The signs are placed at this marks

0m,500m,1000m,1500m,2000m,2500m,3000m,3500m and 4000m