Question

A baker is gathering the ingredients required to make 15 batches of oatmeal cookies and 1 cake. The cake will require one-quarter bag of flour. The baker needs a total of more than 3 but less than 4 bags of flour. What is one possible value for the fraction of one bag of flour required for each batch of cookies?

Answer 1

Let's call the fraction of one bag of flour required for each batch of cookies "x".

The cake requires one-quarter of a bag of flour, which is 0.25 bags of flour.

For 15 batches of oatmeal cookies and 1 cake, the total amount of flour required is:

15 batches * x bags of flour per batch + 0.25 bags of flour for the cake

We know that the total amount of flour required is more than 3 but less than 4 bags of flour:

3 < 15x + 0.25 < 4

Subtracting 0.25 from all parts of the inequality:

2.75 < 15x < 3.75

Dividing all parts of the inequality by 15:

0.1833... < x < 0.25

So one possible value for the fraction of one bag of flour required for each batch of cookies is between 0.1833 and 0.25.

Answer 2

Let's call the fraction of one bag of flour required for each batch of cookies "x".

If the baker is making 15 batches of cookies, then the total amount of flour required for the cookies is 15x.

The cake requires one-quarter bag of flour, which is 0.25 bags of flour.

The total amount of flour required is the amount for the cookies plus the amount for the cake, which is:

15x + 0.25

We know that the total amount of flour required is more than 3 but less than 4 bags of flour. So we can set up the inequality:

3 < 15x + 0.25 < 4

Subtracting 0.25 from all parts of the inequality, we get:

2.75 < 15x < 3.75

Dividing all parts of the inequality by 15, we get:

0.1833... < x < 0.25

Therefore, one possible value for the fraction of one bag of flour required for each batch of cookies is 0.2 or 1/5.