John has two boxes. The first box has 90 spiders. The second box has 44 spiders. Every day, John moves two spiders from the first box to the second box. In how many days will the number of spiders in the second box be greater than the number in the first box?

12 Days

Step-by-step explanation:

Let's make some equations out of what they give us

The first equation would be for the first box

90 - 2x

The first box has 90 spiders initially and 2 get removed everyday (each day is represented by variable x)

The second equation would be for the second box

44 + 2x

The second box has 44 spiders initially and 2 get added everyday

Now, we can set them equal to each other

90 - 2x = 44 + 2x

Solve

46 = 4x

x = 11.5

In 11.5 days the spiders would be equal. But this does not mean we are done. We have to find how many days the number of spiders in the second box will be greater than the number in the first box.

The first day that the number of spiders in the second box will be greater than the number in the first box is 12 days. We just rounded up to get the first whole day that it will be greater.

Check:

90 - 2(12) = 44 + 2(12)

90 - 24 = 44 + 24

66 = 68

90 - 2(11.5) = 44 + 2(11.5)

90 - 23 = 44 + 23

67 = 67

We see here that after 11.5 days there is 67 spiders in each box. We then see that after 12 days the second box has 68 spiders and the first box has 66 spiders.

Hope this helps!!

- Kay :)

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)