I need help please help me. There's a chart that has to have 16boxes. It has to be 4 by 4. Lable boxes that are vertical top to bottom 1,2,3,4 and boxes that are horizontal left to right A,B,C,D. Box 1A has to be 28,Box 1C has to be 34, box 2C has to be 24, and box 2D has to be 12. Now you must make all sides able to add up to 84, both horizontally and vertically.Please help!!!!!!!!!!!!!!!!!!!!!!!!!!
I assume you want to use an arithmetic progression to fill in the square.
16/2 (a + a + 15d) = 84
8(2a + 15d) = 336
2a+15d = 42
If d is an integer, then 15d needs to be even, and less than 42. So,
a = 6
d = 2
and the numbers to be used are
6 8 10 ... 34 36
Here are a couple of squares that meet your restrictions:
28 8 34 14
16 32 24 12
10 18 20 36
30 26 6 22
--------------------
28 8 34 14
30 18 24 12
20 26 16 22
6 32 10 36
Sure, I'd be happy to help you. To create a 4x4 chart with all sides adding up to 84, we can use a step-by-step approach to solve this problem.
First, let's fill in the known values:
| | A | B | C | D |
|---|---|---|---|---|
| 1 | 28| | 34| |
| 2 | | | 24| 12|
| 3 | | | | |
| 4 | | | | |
Now, let's calculate the missing values. We know that each row and each column should add up to 84.
Starting with the first row:
28 + x + 34 + y = 84
Simplifying, we get:
x + y = 22 (1)
Next, let's look at the second row:
x + z + 24 + 12 = 84
Simplifying, we get:
x + z = 48 (2)
Now, let's consider the first column:
28 + v + w + x = 84
Simplifying, we get:
v + w + x = 56 (3)
Finally, the second column:
34 + y + z + w = 84
Simplifying, we get:
y + z + w = 50 (4)
Now we have a system of equations to work with:
Equation (1): x + y = 22
Equation (2): x + z = 48
Equation (3): v + w + x = 56
Equation (4): y + z + w = 50
To solve this system, we can use substitution or elimination methods. I'll use elimination:
From equations (3) and (4), we can subtract equation (4) from equation (3):
(v + w + x) - (y + z + w) = 56 - 50
This simplifies to:
x - y + z = 6 (5)
Now, we have two equations with two variables:
Equation (1): x + y = 22
Equation (5): x - y + z = 6
Adding equation (1) to equation (5):
2x + z = 28 (6)
Now, we can solve equations (2) and (6):
(2) x + z = 48
(6) 2x + z = 28
Subtracting equation (6) from equation (2):
(2x + z) - (2x + z) = 48 - 28
This simplifies to:
0 = 20
Uh-oh! We have encountered an inconsistency in our equations. It seems that there is no solution that satisfies all the given conditions. Thus, it is not possible to fill the chart with numbers such that all sides add up to 84.