Answer:
number of sweet in the bag = 36
Explanation:
Let
x = number of sweet in the bag
He gave 1 to his son
Remaining sweet = x - 1 sweets
1/7 of remaining sweets = 1/7 * (x-1)
= (x-1) / 7
Total sweets given to son = 1 + (x-1) / 7
= (7+x-1) / 7
= (x+6) / 7 (1)
Sweets remaining in the bag after giving to son
= x - {(x+6)/7}
= {7x-(x+6)} / 7
= (7x-x-6) / 7
= (6x-6)/7
He gave 2 sweets to daughter
Remaining sweets
= {(6x-6)/7}-2
= {(6x-6)-14} / 7
= (6x-6-14) / 7
= (6x-20)/7
He gave 1/7 from remaining to his daughter
= (6x-20)/7) * (1/7)
=(6x-20)/49
Total sweets given to daughter
= (6x-20)/49) + 2
= {(6x-20)+98} / 49
= (6x-20+98) / 49
=(6x+78)/49 (2)
Both children have the same number of sweets
Equate equation (1) and (2)
(x+6)/7 = (6x+78)/49
Cross product
(x + 6)49 = 7(6x +78)
49x + 294 = 42x + 546
49x - 42x = 546 - 294
7x = 252
x = 252/7
x = 36
number of sweet in the bag = 36