Question

It was Mrs. Johnson's birthday, and she made her favorite homemade cookies to share with the class. "I hope you all enjoy my homemade cereal crunch cookies. I used a mixture of different cereals to make this. Unique!" says Mrs. Johnson as she saw Joshua raise his hand. "But don't worry! They are all nut free." The class LOVED them. In no time at all the class ate five-sixths of the cookies. "Mrs. Johnson." said Hannah, "you need to do OUR tradition. While we sing happy birthday, you need to eat as many cookies as you can. As the class began to sign, that is just what Mrs. Johnson did. And she was good at it! She ate three-fourths of the cookies that were left. In case you are curious, that was equal to 3 cookies! How many cookies did Mrs. Johnson bring to class that day?

Answer 1

Answer: 24 cookies.

Step-by-step explanation:

the answer to the questions is as below

Let's start by using variables to represent the number of cookies that Mrs. Johnson brought to class. Let's say she brought "x" cookies.

We know that the class ate five-sixths of the cookies, which means that there were only one-sixth of the cookies left. This can be represented as:(1/6)x cookies left

We also know that Mrs. Johnson ate three-fourths of the cookies that were left, which is equal to 3 cookies. We can set up an equation to represent this:

(3/4)(1/6)x = 3

Simplifying this equation, we get:

(1/24)x = 1

x = 24

Therefore, Mrs. Johnson brought 24 cookies to class that day.

Answer 2

Let's work backwards to figure out how many cookies were left after Mrs. Johnson ate 3 cookies:

Before Mrs. Johnson ate the cookies, the class had eaten 5/6 of the cookies, which means that 1/6 of the cookies were left.

Let's call the number of cookies in 1/6 of the batch "x". So the total number of cookies is 6x.

After the class ate 5/6 of the cookies, there were 1/6 of the cookies left, which is x.

Then Mrs. Johnson ate 3/4 of the cookies that were left, which means she ate 3/4*x cookies.

We know that Mrs. Johnson ate 3 cookies, so we can set up the equation: 3 = 3/4*x

Solving for x:

3 = 3/4x

34/3 = x

4 = x

So there were 4 cookies in 1/6 of the batch, which means there were 6 times as many, or 6*4 = 24 cookies in the whole batch.

Therefore, Mrs. Johnson brought 24 cookies to class that day.