At the Natural History museum Paula saw 5 times as many beetles as spiders. She saw 6 more spiders than caterpillars. If Paula saw 50 insects and spiders, how many of each kind did she see?
two house spiders caught 14 flies in theirrespective webs over a week's time. the larger spider caught 2 more flies than the smaller spider.
S+5s+s-6=50
S+5s+s=56
7s=56
S=8
So Paula saw 8 spiders, 40 beetles, and 2 caterpillars
Let's break down the information given:
Let's say the number of spiders Paula saw is "s".
Then the number of beetles Paula saw is 5 times the number of spiders, which is 5s.
And Paula saw 6 more spiders than caterpillars. So the number of caterpillars she saw is s - 6.
We know that the total number of insects and spiders Paula saw is 50. So the equation is:
s + 5s + s - 6 = 50.
Combining like terms, we get:
7s - 6 = 50.
Adding 6 to both sides, we get:
7s = 56.
Dividing both sides by 7, we get:
s = 8.
Therefore, Paula saw 8 spiders, 5s = 5 x 8 = 40 beetles, and s - 6 = 8 - 6 = 2 caterpillars.
To solve this problem, we can set up a system of equations. Let's represent the number of beetles as "b", the number of spiders as "s", and the number of caterpillars as "c".
From the given information, we have two equations:
1) b = 5s (Paula saw 5 times as many beetles as spiders)
2) s = c + 6 (Paula saw 6 more spiders than caterpillars)
We also know that the total number of insects and spiders Paula saw is 50:
b + s + c = 50
Now, let's substitute equation 1 and equation 2 into the third equation:
5s + s + (s - 6) = 50
7s - 6 = 50
7s = 56
s = 8
Using this value of "s", we can substitute it back into equation 2:
8 = c + 6
c = 2
Finally, to find the value of "b", we substitute the value of "s" into equation 1:
b = 5(8)
b = 40
Therefore, Paula saw 40 beetles, 8 spiders, and 2 caterpillars at the Natural History museum.