How many marbles?
Sophie has a bag of marbles. She gives half of them to her friend Alex. Then, she gives a third of what she has left to Ben. After that, she gives a quarter of the remaining marbles to Clara. If she ends up with 18 marbles, how many marbles did Sophie have at the start?
Sophie gave a quarter of her marbles to Clara, and kept 18.
ReplyDeleteThis means 18 marbles is three-quarters of what she had before giving to Clara.
Let’s call that amount x.
So:
(3/4) × x = 18
Multiply both sides by 4:
3x = 72
Divide by 3:
x = 24
So, she had 24 marbles before giving to Clara.
Step 2: Ben
She gave a third of her marbles to Ben before that, and was left with 24 marbles.
So 24 marbles is two-thirds of what she had before giving to Ben.
Let’s call that amount y.
(2/3) × y = 24
Multiply both sides by 3:
2y = 72
Divide by 2:
y = 36
She had 36 marbles before giving to Ben.
Step 3: Alex
She gave half of her original marbles to Alex, then had 36 marbles left.
So 36 marbles is half of her starting amount.
Let’s call her starting amount z.
(1/2) × z = 36
Multiply both sides by 2:
z = 72