The Missing Marbles
Sophie has some marbles. She gives 1/3 of them to her friend Emma and then gives 12 more to her brother. She is left with 20 marbles.
How many marbles did Sophie 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 Sophie had at the start be x.
ReplyDeleteShe gave one-third to Emma:
That’s x ÷ 3
She then gave 12 more to her brother.
She is left with 20 marbles.
So:
x – (x ÷ 3) – 12 = 20
Step 1: Combine terms
x – x⁄3 = (3x – x)⁄3 = 2x⁄3
So:
(2x ÷ 3) – 12 = 20
Step 2: Add 12 to both sides
(2x ÷ 3) = 32
Step 3: Multiply both sides by 3
2x = 96
Step 4: Divide by 2
x = 48
Final Answer: Sophie had 48 marbles at the start.