Question

Program X has an annual cost of $35000, and, in return, is expected to save Company C $40,000 during the first year. Assuming the cost and savings are equally distributed across each month, after how many months will the company recover its investment in Program X?

1.5, 5.5, 10.5, 12, or 14 months?

Answer 1

For the answer to the question above,
The program has an annual cost of $35,000 and will generate $40,000 savings the first year. 

$35,000 / $40,000 = .875
.875 x 12 months = 10.5 months
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Answer 2

The number of months in which the company recover its investment in Program X is given by: Option C: 10.5 months (10 and a half months)

How to interpret the division?

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

Thus,  $a \div b = a$ divided in b equal parts.

Also, we can write: $a \div b = a \times \dfrac{1}{b}$

(it is since a = a times 1 so $a/b = 1 \times (a/b) = (1/b) \times a$ )

We're provided that:

• Annual cost of program X = $35,000
• Annual savings through Program X = $40,000
• Cost and savings are equally distributed across each month.

Splitting savings by program in each month(12 months in an year) gives us:

Savings per month = 40000/12

Let in x months, the company recovers its investment in program X.

At that moment, the savings would equate to the cost of the program X.

For m months, the savings would be: $\dfrac{40000}{12} \times m$

This is equal to cost of the program X, that is 35000, or:

$\dfrac{40000}{12}\times m = 35000\\\\\text{Multiplying 12 on both the sides}\\40000 \times m = 420000\\\\\text{Dividing both the sides by 40000}\\\\m = \dfrac{420000}{40000} = 10.5$

Thus, the number of months in which the company recover its investment in Program X is given by: Option C: 10.5 months (10 and a half months)

Learn more about division here:

https://brainly.com/question/26411682