Chapter 6.4, Problem 25PPS

a.

To determine

To find: The number of tubes that each girl plan to bake and the time that each used to oven.

Answer to Problem 25PPS

M plan to bake 7 tubes of cookies and J plans to bake 3 tubes of cookies.

Time taken by M is 56 mins and time take by J is 36 mins.

Explanation of Solution

Given:

They need to bake 264 cookies. Each tube of cookies contains 36 cookies. It takes 8 minutes to bake a container of cookies, but it takes 12 minutes for the person J.

Calculation:

Let M bakes $x$ tubes of cookies and J bakes $y$ tubes of cookies.

Then, for the time constraint, the equation becomes $8x+12y=90$ .

For the number of cookies, the equation can be written as $\frac{4}{5}\left(36x\right)+\frac{1}{1.5}\left(36y\right)=264$ .

So, M plan to bake 7 tubes of cookies and J plans to bake 3 tubes of cookies.

Time taken by M is $7\times 8=56\text{ mins}$ and time take by J is $3\times 12=36\text{ mins}$ .

b.

To determine

To explain the solution process.

Explanation of Solution

Given:

They need to bake 264 cookies. Each tube of cookies contains 36 cookies. It takes 8 minutes to bake a container of cookies, but it takes 12 minutes for the person J.

Calculation:

Let M bakes $x$ tubes of cookies and J bakes $y$ tubes of cookies.

Then, for the time constraint, the equation becomes $8x+12y=90$ .

For the number of cookies, the equation can be written as $\frac{4}{5}\left(36x\right)+\frac{1}{1.5}\left(36y\right)=264$ .

Solving the two equation gives:

  $x=6.6525,y=3.125$ .

Rounding off to the nearest integer gives: $x=7,y=3$ .

So, M plan to bake 7 tubes of cookies and J plans to bake 3 tubes of cookies.

Time taken by M is $7\times 8=56\text{ mins}$ and time take by J is $3\times 12=36\text{ mins}$ .

c.

To determine

To write the assumptions made in solution process.

Explanation of Solution

The following are the assumptions made in the solution process:

1. Both M and J cannot bake their cookies simultaneously.
2. Girls were able to make the entire tube of cookies in one batch.
3. The amount of time required to transfer baked cookies from oven and unbaked cookies to the oven is negligible.