Class 6 Math book | Pg: 172 (b) | Solution

 Let's solve this step by step by thinking boxes as variables :

1. A + B = 15

2. A + C = 12

3. B - D = 2

4. C + D = 15

Let's first solve equations 1 and 2:

1. A + B = 15

2. A + C = 12

Subtract equation 2 from equation 1 to eliminate A:

(A + B) - (A + C) = 15 - 12

Simplify:

B - C = 3

Now, we have:

5. B - C = 3

Next, let's solve equations 3 and 4:

3. B - D = 2

4. C + D = 15

Add equation 3 and equation 4 to eliminate D:

(B - D) + (C + D) = 2 + 15

Simplify:

B + C = 17

Now, we have:

6. B + C = 17

We now have two equations:

5. B - C = 3

6. B + C = 17

Add equations 5 and 6 together to eliminate C:

(B - C) + (B + C) = 3 + 17

Simplify:

2B = 20

Now, divide by 2:

B = 10

Now that we have the value of B, we can find the values of A, C, and D:

From equation 1:

A + 10 = 15

A = 15 - 10

A = 5

From equation 2:

5 + C = 12

C = 12 - 5

C = 7

From equation 3:

10 - D = 2

D = 10 - 2

D = 8

So, the values of A, B, C, and D are:

A = 5

B = 10

C = 7

D = 8