Answer
a.
5 22 18
28 15 2
12 8 25
The sums are 45.
b.
4 9 8
11 7 3
6 5 10
The sums are 21.
Work Step by Step
The square looks like this:
5 _ 18
_ 15 _
_ _ 25
A magic square gives the same result for sums of all digits in any row, column or diagonal.
a.
We have all the digits of one diagonal; therefore we know that the sum of our square is $5+15+25=45$.
With that, we can calculate the upper middle space by looking at the first row:
$45-18-5=22$
the middle right space looking at the last column:
$45-25-18=2$
and the bottom left space looking at it's diagonal:
$45-15-18=12$
Now the square looks like this:
5 22 18
_ 15 2
12 _ 25
The two remaining spaces are:
$45-15-2=28$
$45-15-22=8$
This is the full magic square:
5 22 18
28 15 2
12 8 25
b.
The numbers of the letters in each word for the numbers in the square are as follows:
five – 4
twenty-two – 9
eighteen – 8
twenty-eight-11
fifteen – 7
two – 3
twelve - 6
eight – 5
twenty-five – 10
putting these numbers back in the square, we get:
4 9 8
11 7 3
6 5 10
The sums for each row, column and diagonal are:
$4+9+8=21$
$11+7+3=21$
$6+5+10=21$
$4+11+6=21$
$9+7+5=21$
$8+3+10=21$
$4+7+10=21$
$6+7+8=21$
This proves this square is a magic square too.
