Marble mysteries
Tom had some marbles. He gave half of them to Sarah. Then he gave one-third of the remaining marbles to James. After that, he had 20 marbles left.
How many marbles did Tom have at the start?
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 the number of marbles Tom started with be x.
ReplyDeleteHe gave half to Sarah:
Marbles left = x ÷ 2
Then he gave one-third of the remaining to James:
One-third of x ÷ 2 = (1/3) × (x ÷ 2) = x ÷ 6
Marbles left after giving to James =
x ÷ 2 – x ÷ 6
Simplify:
(x ÷ 2) – (x ÷ 6) = (3x – x) ÷ 6 = 2x ÷ 6 = x ÷ 3
We’re told that after all this, he had 20 marbles left, so:
x ÷ 3 = 20
→ Multiply both sides by 3:
x = 60