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

 

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

1. A + B = 10

2. A + C = 17

3. B + D = 10

4. C - D = 12

From equations 1 and 3, we can see that A = 10 - B and D = 10 - B.

Now, substitute these expressions for A and D into equations 2 and 4:

2. (10 - B) + C = 17

4. C - (10 - B) = 12

Simplify equation 2:

10 - B + C = 17

Now, add B to both sides:

C = 17 - 10 + B

C = 7 + B

Now, simplify equation 4:

C - 10 + B = 12

C + B = 12 + 10

C +B = 22

Now, we have two equations involving C and B:

C = 7 + B

C + B = 22

Substitute the value of C from the first equation into the second equation:

(7 + B) + B = 22

Combine like terms:

2B + 7 = 22

2B = 22 - 7

2B = 15

B = 15 / 2

B = 7.5

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

From equation 1:

A + B = 10

A + 7.5 = 10

A = 10 - 7.5

A = 2.5

From equation 2:

A + C = 17

2.5 + C = 17

C = 17 - 2.5

C = 14.5

From equation 3:

B + D = 10

7.5 + D = 10

D = 10 - 7.5

D = 2.5

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

A = 2.5

B = 7.5

C = 14.5

D = 2.5