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?
Free Online 11+ Maths Tutoring – Open to All
Free Online 11+ Maths Tutoring – Open to All Hi! I’m Rithvik Muthuvelu , a GCSE student at King Edward’s School, Birmingham , and I’m offering free weekly online maths sessions to help students prepare for the 11+ entrance exams . These sessions are open to anyone who wants to improve their maths skills—no school restrictions. What You’ll Get Free weekly online maths classes Focused 11+ preparation : problem-solving, arithmetic, word problems, exam strategies Small-group format for better interaction Ideal for Year 4 and Year 5 students How to Join Weekly Session: Saturdays at 2:00 PM — COMING SOON! Google Meet Link: https://meet.google.com/nrk-iwmh-gij Contact Email: rithvikmu1@gmail.com If your child is preparing for the 11+ and would like extra support, feel free to join the class or get in touch. Looking forward to helping more students learn and grow! — Rithvik Muthuvelu
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.