An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Define variables for the missing values: x , y , z , and w .
Use row and column totals to create equations involving these variables.
Solve the system of equations to find the values of x , y , z , and w .
The missing values are x = 1482 , y = 93 , z = 65 , w = 17476 .
Explanation
Understanding the Problem We are given a table with missing values representing military personnel categorized by pay grade and marital status. Our goal is to fill in these missing values using the provided row and column totals. We will use basic arithmetic to find the missing numbers.
Defining Variables Let's denote the missing values as follows:
The missing value in row M 2 (Single with children) and column G 2 (Officer) as x .
The missing value in row M 2 (Single with children) and column G 3 (Warrant) as y .
The missing value in row M 3 (Joint service marriage) and column G 3 (Warrant) as z .
The missing value in row M 3 (Joint service marriage) and column 'Total' as w .
The total of column G 2 as T .
Calculating x + y From row M 2 , we have the equation: 14786 + x + y = 16361 Solving for x + y :
x + y = 16361 − 14786 = 1575
Calculating y + z From column G 3 , we have the equation: 72 + y + z + 1427 = 1657 Solving for y + z :
y + z = 1657 − 72 − 1427 = 158
Relating z and w From row M 3 , we have the equation: 14723 + 2688 + z = w Simplifying: 17411 + z = w
Calculating w From the 'Total' column, we have the equation: 132102 + 16361 + w + 158434 = 324373 Solving for w :
w = 324373 − 132102 − 16361 − 158434 = 17476
Calculating z Now we can substitute w = 17476 into the equation 17411 + z = w :
17411 + z = 17476 Solving for z :
z = 17476 − 17411 = 65
Calculating y Substitute z = 65 into the equation y + z = 158 :
y + 65 = 158 Solving for y :
y = 158 − 65 = 93
Calculating x Substitute y = 93 into the equation x + y = 1575 :
x + 93 = 1575 Solving for x :
x = 1575 − 93 = 1482
Calculating Total of G2 Finally, let's calculate the total of column G 2 :
T = 13919 + x + 2688 + 32036 = 13919 + 1482 + 2688 + 32036 = 50125 So, the total of column G 2 is 50125.
Final Answer The missing values are:
x = 1482
y = 93
z = 65
w = 17476
T = 50125 Therefore, the completed table would have the following values in the missing cells: 1482, 93, 65, 17476.
Examples
This type of problem, where you need to fill in missing data based on totals, is similar to balancing budgets or tracking inventory. For example, a store might use a table like this to keep track of how many items they have in stock, how many they've sold, and how many they need to order. By knowing the totals for each row and column, they can quickly figure out any missing numbers and make sure their inventory is accurate. This helps them make informed decisions about what to order and how to manage their resources effectively.
