Siti has some red beads and blue beads. 3/5 of all her beads are red. She gives away 30 red beads and receives 10 blue beads. After this, 1/2 of all her beads are red. How many beads did Siti have at first?
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Worked Solution
Step 1: Let the total number of beads at first = T. Red beads at first = 3T/5.
Step 2: After giving away 30 red beads and receiving 10 blue beads, the new total = T − 30 + 10 = T − 20. Red beads now = 3T/5 − 30.
Step 3: Red beads are now 1/2 of the new total: 3T/5 − 30 = 1/2 × (T − 20).
Step 4: Multiply both sides by 10: 6T − 300 = 5(T − 20) = 5T − 100. So 6T − 5T = −100 + 300, giving T = 200.
Step 5: Check — Red at first: 3/5 × 200 = 120. After transfer: Red = 90, Total = 180. 90/180 = 1/2. ✓
Answer: 200
Correct answer: 200
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