In the magic square shown (I'll type it out), the sum of the numbers in each row, column, and diagonal are the same. Five of these numbers are represented by v,w,x,y, and z. Find y + z.

Question

In the magic square shown (I'll type it out), the sum of the numbers in each row, column, and diagonal are the same. Five of these numbers are represented by v,w,x,y, and z. Find y + z.

Here's what the magic square looked like. I'll type semi-colons to separate each "square."

v; 24; w
18; x; y
25; z; 21

I don't know how to solve this at all. Considering that all of the other problems on this worksheet had to do with systems of 3 equations with 3 variables, I'm assuming I'll have to make a system of equations. How would I find this information in the magic square?

Answer 1

To find the value of y + z in the magic square, we need to first understand the concept of a magic square. In a magic square, the sum of the numbers in each row, column, and diagonal is the same. Therefore, we can set up equations based on this property to find the values of the variables.

Let's start by labeling the numbers in the magic square as follows:

v 24 w
18 x y
25 z 21

Since the sum of each row is the same, we can set up the following equation:

v + 24 + w = 18 + x + y = 25 + z + 21

Now, to find y + z, we can equate two of these equations that contain y and z. Let's equate the first and third equations:

v + 24 + w = 25 + z + 21

Now, we can solve this equation to find the values of y + z.

First, let's simplify the equation:

v + w + 24 = z + 46

Now, rearrange the equation to isolate y + z:

y + z = v + w - 46

So, to find y + z, we need to know the values of v and w.

This is where we encounter a problem. Without any additional information or context, we cannot determine the values of v and w. Therefore, we cannot find the exact value of y + z in this magic square.

However, if you are given more information or constraints regarding the values of v and w, please provide it, and we can proceed to find the solution.

Answer 2

last row = second column

25 + z + 21 = 24 + x + z
x = 22

second row = last row (we now know x=22)
18+22+y = 25+z+21
y = z + 6 #1

first row = third colums
v+24+w = w+y+21
y=v+3 #2

first row = right diagonal
v+24+w = 25+x+w
v+24 = 25+22
v = 23

then in #2 y = 23 + 3 = 26

we now know the sum of each row from the second row:
18+22+26 = 66

so what do we have so far ?
23 24 w
18 22 26
25 z 21

from that w = 66-23-24 = 19
z = 66-25-21 = 20

check:
23 24 19
18 22 26
25 20 21 OK!

Answer 3

There was really no method to what I did

I noticed that the last row was a good one to use, since it contained only one variable

from there it was just "hit or miss"
there may very well be a better way.