Ravi had some bookmarks. He gave 3/8 of them to his classmates and 2/5 of the remainder to his teachers. He had 33 bookmarks left. How many bookmarks did Ravi have at first?
Show Worked Solution
Worked Solution
Step 1: Find the fraction of bookmarks remaining after giving to classmates.
Ravi gave 3/8 to classmates, so 1 − 3/8 = 5/8 remained.
Step 2: Find the fraction remaining after giving to teachers.
He gave 2/5 of the remainder to teachers, so 1 − 2/5 = 3/5 of the remainder was left.
Fraction of original left = 5/8 × 3/5 = 15/40 = 3/8
Step 3: Use the leftover fraction to find the original total.
3/8 of T = 33
T = 33 ÷ 3/8 = 33 × 8/3 = 88
Step 4: Verify.
Classmates received: 3/8 × 88 = 33. Remainder: 55.
Teachers received: 2/5 × 55 = 22. Left: 55 − 22 = 33. ✓
Answer: 88
Correct answer: 88
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