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NikAS [45]
4 years ago
7

A recent physical inventory at a department store reports a merchandise value of $875,435. The merchandise book value was $907,3

40. The merchandise sales were $1,988,345. What is the shrinkage as a percentage of sales? (Shrinkage is the difference between the book value and the merchandise value from a physical inventory.)
Mathematics
1 answer:
Vlad [161]4 years ago
5 0

Answer:

The shrinkage as a percentage of sales is 1.6%.

Step-by-step explanation:

In order to find the percentage of the sales that can be contributed to shrinkage, we first need to find the amount of shrinkage between the book value ($907,340) and the physical inventory ($875,435).  The difference between these two values is $31,905.  With this value of shrinkage, I then divide by the total amount in sales, which is $1,988,345.  This would give me an overall percentage of 1.6%, which represents the shrinkage as a percentage of sales.  

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$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}

Solution:

Given expression:

$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}

To solve the given expression:

First simplify: \frac{50-2 w^{2}}{3 w^{2}+9 w-30}

$\frac{50-2 w^{2}}{3 w^{2}+9 w-30}=-\frac{2(w+5)(w-5)}{3(w-2)(w+5)}

Cancel the common factor (w + 5).

                      $=-\frac{2(w-5)}{3(w-2)}

Now substitute this in the given expression.

$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{2(w-5)}{3(w-2)} \cdot \frac{w^{2}+5 w-14}{6 w-30}

Multiply the fractions \frac{a}{b} \cdot \frac{c}{d}=\frac{a \cdot c}{b \cdot d}

                               $=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{3(w-2)(6 w-30)}

Factor the denominator 3(w-2)(6 w-30) =18(w-2)(w-5)

                               $=-\frac{2(w-5)\left(w^{2}+5 w-14\right)}{18(w-2)(w-5)}                        

Cancel the common factor 2(w – 5).

                               $=-\frac{w^{2}+5 w-14}{9(w-2)}

Factor the numerator w^{2}+5 w-14=(w-2)(w+7)

                               $=-\frac{(w-2)(w+7)}{9(w-2)}

Cancel the common factor (w – 2).

                               $=-\frac{w+7}{9}

$\frac{50-2 w^{2}}{3 w^{2}+9 w-30} \cdot \frac{w^{2}+5 w-14}{6 w-30}=-\frac{w+7}{9}

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3 years ago
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