How many sweets in the jar
Sophie had a jar of sweets. She gave half of them to her friend Lucy. Then she gave a third of what was left to her brother. Finally, she ate 6 of the remaining sweets and found that she had only 10 sweets left.
How many sweets did Sophie have at the beginning?
Step 1: Gave half to Lucy
ReplyDeleteSweets left = x ÷ 2 = (1/2)x
Step 2: Gave 1/3 of the remainder to her brother
She gives 1/3 of (1/2)x = (1/3) × (1/2)x = (1/6)x
Sweets left after this = (1/2)x - (1/6)x = (3/6 - 1/6)x = (1/3)x
Step 3: She eats 6 sweets
Sweets left after eating = (1/3)x - 6
We’re told she ends up with 10 sweets, so:
(1/3)x - 6 = 10
Add 6 to both sides:
(1/3)x = 16
Multiply both sides by 3:
x = 48