9514 1404 393
Answer:
A = pentagon = 6
B = 5-pointed star = 8
C = rectangle = 4
D = spiral = 3
Step-by-step explanation:
Starting in the upper left corner, name the shapes A, B, C, D clockwise in the 2×2 square in that corner. Then we have ...
A = pentagon
B = 5-pointed star
C = rectangle
D = spiral
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It turns out to be convenient to look at rows and columns with two of each shape.
Row 2: 2(C+D) = 14 ⇒ C+D = 7
We can use that in column 2 to find B:
B +C +B +D = 23 ⇒ 2B +(C+D) = 23 ⇒ 2B = 16 ⇒ B = 8
This lets us find D:
Row 4: 3D +B = 17 ⇒ 3D +8 = 17 ⇒ 3D = 9 ⇒ D = 3
So, C can now be found:
C+D = 7 ⇒ C +3 = 7 ⇒ C = 4
Finally, we can find A:
Row 1: A +2B +D = 25 ⇒ A +2(8) +3 = 25 ⇒ A = 6
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In summary, the numerical values are ...
A = pentagon = 6
B = 5-pointed star = 8
C = rectangle = 4
D = spiral = 3
