Question

Kiran is recalling Easter egg hunts from her childhood. She remembers that there were 2 Easter egg hunts where

she found 8 eggs each and 4 Easter egg hunts where she found 11leggs each. She also knows that she averaged
11.6 eggs per Easter egg hunt. This information is summarized in the table below.
Fill in the missing blank with the number of hunts where Kiran found 14 eggs.

Answer 1

In 4 Easter egg hunts she found 14 eggs

Explanation:

The table is missing, but the thing we need to complete in the table is a number X, where X is the number of easter egg hunts where she found 14 eggs.

We already know that:

2 times she found 8 eggs

4 times she found 11 eggs

X times she found 14 eggs.

And we also know that the average is 11.6 eggs.

Where the average can be computed as:

The quotient between all the eggs she found in all the Easter egg hunts, and the total number of Easter egg hunts were she attended.

She got a total of: 2*8 eggs + 4*11 eggs + X*14 eggs.

And she attended a total of 2 + 4 + X Easter egg hunts, then:

This is then:

`avg = (2*8 + 4*11 + X*14)/(2 + 4 + X) = 11.6`

Now we just need to solve the above equation for X.

We can rewrite this as:

`2*8 + 4*11 + X*14 = 11.6*(2 + 4 + X)`

`16 + 44 + X*14 = 11.6*(6 + X)`

`60 + X*14 = 11.6*(6 + X) = 11.6*X + 69.6`

`(14 - 11.6)*X = 69.6 - 60`

`2.4*X = 9.6`

X = 9.6/2.4 = 4

This means that in 4 Easter egg hunts she found 14 eggs.