How many marbles?
Sarah had a bag of marbles. She gave half of them to her friend Tom. Then, she gave a third of the remaining marbles to her sister. If she had 18 marbles left after that, how many marbles did she have at the beginning?
Word Problem
A bridge is built across a river. One quarter of the bridge is over the left bank of the river and one third of the bridge is over the right bank. The river is 120 m wide. How long is the bridge?
Let’s work backwards from what we know.
ReplyDeleteStep 1: Let’s say after giving to her sister, she had 18 marbles left.
That means the 18 marbles are two-thirds of what she had after giving to Tom, because she gave 1/3 to her sister.
Let that amount be R (remaining after giving to Tom).
So:
(2/3) × R = 18
Multiply both sides by 3:
2R = 54
Now divide by 2:
R = 27
So, Sarah had 27 marbles after giving half to Tom.
That means the 27 marbles are half of her original number.
So original number = 27 × 2 = 54