Answer:
37.5
Step-by-step explanation:
so x% of 40 is 15
the equation for that is
x/100 * 40 = 15
40x/100 = 15
multiply 100 on both sides
40x = 1500
divide 40 on both sides
37.5
37.5% of 40 is 15
First write the equation:
1/2x + 5 = 6
Then subtract five from both sides:
1/2x = 1
Multiply both sides by 2:
x = 2
Answer:


Step-by-step explanation:
Given
See attachment for complete question
Solving (a): The entry C22
First, matrix C represents the inventory at the end of July.
The entry of C is calculated as:

i.e.
![C = \left[\begin{array}{ccc}543&356&643\\364&476&419\\376&903&409\end{array}\right] - \left[\begin{array}{ccc}102&78&97\\98&87&59\\54&89&79\end{array}\right]](https://tex.z-dn.net/?f=C%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D543%26356%26643%5C%5C364%26476%26419%5C%5C376%26903%26409%5Cend%7Barray%7D%5Cright%5D%20%20-%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D102%2678%2697%5C%5C98%2687%2659%5C%5C54%2689%2679%5Cend%7Barray%7D%5Cright%5D)
![C = \left[\begin{array}{ccc}543-102&356-78&643-97\\364-98&476-87&419-59\\376-54&903-89&409-79\end{array}\right]](https://tex.z-dn.net/?f=C%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D543-102%26356-78%26643-97%5C%5C364-98%26476-87%26419-59%5C%5C376-54%26903-89%26409-79%5Cend%7Barray%7D%5Cright%5D)
![C = \left[\begin{array}{ccc}441&278&546\\266&389&360\\322&814&330\end{array}\right]](https://tex.z-dn.net/?f=C%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D441%26278%26546%5C%5C266%26389%26360%5C%5C322%26814%26330%5Cend%7Barray%7D%5Cright%5D)
Item C22 means the entry at the second row and the second column.
From the matrix

Solving (b): The maximum A31 possible.
From the given data, we have:
![Inventory = \left[\begin{array}{ccc}543&356&643\\364&476&419\\376&903&409\end{array}\right]](https://tex.z-dn.net/?f=Inventory%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D543%26356%26643%5C%5C364%26476%26419%5C%5C376%26903%26409%5Cend%7Barray%7D%5Cright%5D)
![Unit\ Sales = \left[\begin{array}{ccc}102&78&97\\98&87&59\\54&89&79\end{array}\right]](https://tex.z-dn.net/?f=Unit%5C%20Sales%20%3D%20%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D102%2678%2697%5C%5C98%2687%2659%5C%5C54%2689%2679%5Cend%7Barray%7D%5Cright%5D)
From the matrices above.
A31 means entry at the 3rd row and 1st column.
So, the possible values of A31 are:

and

By comparison, 376 > 54
So:
Remark
They are travelling in opposite directions. Their distances will be added until that distance = 462 miles.
You need only add the r*t values together. You do not need to find the distance.
Givens
d = 462 miles
r1 = 115 mph
r2 = 95 mph
t = the time each was traveling.
Formula
r1 * t + r2*t = d
Substitute and solve
95 * t + 115 * t = 462 Add the like terms on the left.
210 * t = 462 Divide by 210
t = 462 / 210
t = 2.2 hours.
t = 2 1/5 hours
t = 2 hours and 12 minutes
All three answers are the same.