A crew of spiders moved into the scary old house and started working at once. They spun 2 webs on the first night, and 7 webs on the second night. On the third night they wove 12 webs. Every night they made 5 more webs than they had made the night before. If the spiders kept spinning in this way, on what night did they spin their 60th web?

Question

A crew of spiders moved into the scary old house and started working at once. They spun 2 webs on the first night, and 7 webs on the second night. On the third night they wove 12 webs. Every night they made 5 more webs than they had made the night before. If the spiders kept spinning in this way, on what night did they spin their 60th web?

--------------------------------------------------------------------------------

Answer 1

2 + 7 + 12 + 17 + 22 = 60

Answer 2

To solve this problem, we need to find the night when the spiders spun their 60th web. We can start by finding a pattern in the number of webs spun each night.

From the given information, we know that the spiders spun 2 webs on the first night, 7 webs on the second night, and 12 webs on the third night. On each subsequent night, the spiders spun 5 more webs than they did the previous night.

So, we can summarize the number of webs spun each night using the following pattern:

Night 1: 2 webs
Night 2: 7 webs
Night 3: 12 webs
Night 4: 17 webs
Night 5: 22 webs
Night 6: 27 webs
Night 7: 32 webs
Night 8: 37 webs
Night 9: 42 webs
Night 10: 47 webs
Night 11: 52 webs
Night 12: 57 webs

We can observe that the spiders spin an additional 5 webs each night. By continuing this pattern, we can find the number of webs they spun on subsequent nights until we reach the night when they spun their 60th web.

However, this is a repetitive and time-consuming process. Instead, we should use an algebraic approach to solve the problem.

Let's consider the number of webs spun on the nth night, denoted by W(n).

Using the given information, we know that W(1) = 2, and on each subsequent night, the spiders spun 5 more webs than they did the previous night. This means that:

W(2) = W(1) + 5
W(3) = W(2) + 5
W(4) = W(3) + 5

Generalizing this pattern, we can write:

W(n) = W(n-1) + 5

We want to find the value of n when W(n) = 60.

Setting W(n) = 60, we can solve the equation:

60 = W(n-1) + 5

Subtracting 5 from both sides:

55 = W(n-1)

By setting W(n-1) = 55, we can use the formula W(n) = W(n-1) + 5 to find the value of n.

W(n) = 55 + 5 = 60

Therefore, the spiders spun their 60th web on the nth night, n = 12.

Answer: The spiders spun their 60th web on the 12th night.