MHB V.02.Binary operator by a*b=a+8b

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The binary operator * is defined as a*b = a + 8b. Calculations for specific values show that 3*5 equals 43, 7*7 equals 83, and 5*3 equals 29. However, there is an error in the calculation for x*z, which should equal x + 8z, resulting in 63 instead of 83. The discussion emphasizes the importance of correctly applying the operator in various scenarios. Overall, the calculations demonstrate the operator's consistent application except for the noted discrepancy.
karush
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Define the binary operator * by:
$a*b=a+8b$
Find each of the following

(the only thing I knew to do here was plug in)
[a.] $3*5\quad =3+8(5)=3+40=43$
[b.] $7*7\quad =7+8(7)=7+56=83$
[c.] $5*3\quad =5+8(3)=5+24=29$
[d.] $x*z\quad =x+8z$
 
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$7+56=63\ne83$. The rest is correct.
 
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Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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