What is the correct way to break 12 into parts and multiply each part by 6?

By the use of algebra.

Step-by-step explanation:

You wish to break the quantity '12' into parts (number of parts not specified) and multiply each part by 6.

If you didn't want to break 12 into parts, the straight method would be to simply multiply 12 by 6.    12 × 6 = 72

Breaking 12 into 12 parts, you have

X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂

In this case, X₁ represents the first unit of the number 12.  X₂ represents the second unit of the number 12.   X₁₂ represents the last unit of the number 12.

Hence, X₁ + X₂ + X₃ + X₄ + X₅ + X₆ + X₇ + X₈ + X₉ + X₁₀ + X₁₁ + X₁₂ = 12

Each X value is the number 1; just that it's in 12 places and each case has a separate identity.

Each X value can then be multiplied by 6 and the sum of all would be 72.

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.