How many marbles
Sophie has a box of marbles. She gives half of her marbles to her friend Liam. Then she gives one-third of the remaining marbles to her cousin Mia. After that, Sophie has 18 marbles left.
How many marbles did Sophie have at the start?
Sophie gives away portions of her marbles in steps. Let's find out how many she had initially.
ReplyDeleteStep 1: Define the Unknown
Let x be the number of marbles Sophie had at the start.
Step 2: Account for Liam's Share
She gives half of her marbles to Liam:
Marbles left = x/2
Step 3: Account for Mia's Share
She gives one-third of the remaining marbles to Mia:
Marbles given to Mia = (1/3) × (x/2) = x/6
Marbles left after Mia = (x/2) - (x/6)
Find a common denominator (6):
(3x/6) - (x/6) = 2x/6 = x/3
We know Sophie now has 18 marbles left:
x/3 = 18
Step 4: Solve for x
Multiply both sides by 3:
x = 54
Final Answer:
Sophie originally had 54 marbles.