number of counters in box A = 17
number of counters in box B = 19
number of counters in box C = 27
Solution:
Given that three boxes box A, box B, box C
Let "a" be the number of counters in box A
Let "b" be the number of counters in box B
Let "c" be the number of counters in box C
Total counters in 3 boxes = 63
counters in box A + counters in box B + counters in box C = 63
a + b + c = 63 -- eqn 1
The total number of counters in box A and box B is 36
counters in box A + counters in box B = 36
a + b = 36 -------- eqn 2
The difference between the number of counters in box A and box C is 10
counters in box C - counters in box A = 10
c - a = 10 ---------- eqn 3
Let us solve eqn 1 , 2, 3 to get values of "a" , "b" and "c"
Substitute eqn 2 in eqn 1
a + b + c = 63
36 + c = 63
c = 27
Substitute c = 27 in eqn 3
27 - a = 10
a = 27 - 10 = 17
a = 17
Substitute a = 17 in eqn 2
a + b = 36
17 + b = 36
b = 19
Thus the number of counters in box A = 17
number of counters in box B = 19
number of counters in box C = 27