27. each circle contains a number so that the calculations are correct. what is the sum of the numbers in…

Explanation:

Step1: Define variables for the circles

Let $W_1$ and $W_2$ be the white circles, and $G_1$ and $G_2$ be the gray circles.

Step2: Set up equations from the grid

From the rows:

1. $W_1 + G_1 = 16$
2. $G_2 + W_2 = 10$ From the columns:
3. $W_1 - G_2 = 4$
4. $G_1 + W_2 = 10$

Step3: Sum the row equations

Add equation 1 and equation 2: $(W_1 + G_1) + (G_2 + W_2) = 16 + 10 = 26$

Step4: Sum the column equations

Add equation 3 and equation 4: $(W_1 - G_2) + (G_1 + W_2) = 4 + 10 = 14$

Step5: Solve for the sum of gray circles

Let $S_G = G_1 + G_2$ and $S_W = W_1 + W_2$. From Step 3: $S_W + S_G = 26$ From Step 4: $S_W + G_1 - G_2 = 14$. This is not directly helpful. Let's use equations 1 and 3 to find $G_1$ and $G_2$ in terms of $W_1$: $G_1 = 16 - W_1$ $G_2 = W_1 - 4$

Step6: Calculate the sum of gray circles

$G_1 + G_2 = (16 - W_1) + (W_1 - 4)$ $G_1 + G_2 = 16 - 4 = 12$

Answer:

(B) 12