Practise the method.
Example 1
Three clubs share funding. Initially A:B=4:5 and B:C=5:8. A then gives 41 of its own allocation to C; B keeps its allocation. C now has $456 more than A. How many dollars were allocated in total?
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Answer: 1292
- The linked ratio is 4:5:8.
- Write allocations as 4k,5k and 8k.
- After the transfer, C−A=(4+48)k=456
- k=76.
- Total funding is 17k=1292.
Example 2
Teams A:B have workers in the ratio 5:6. Each A worker makes 8 parts per hour; each B worker makes 10. During a 6−hour shift, B stops for 2 hours while A works throughout. They make 3840 parts. Next, 2 workers move from A to B and take B's rate. Both teams now work without breaks. How many hours will 1167 further parts take? Give an exact fraction if needed.
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Answer: 268389
- Write initial worker counts as 5k and 6k.
- The first shift gives (5×8×6+6×10×4)k=3840
- k=8.
- After the transfer, the hourly rate is (38)×8+(50)×10=804.
- Divide 1167 by 804.
Example 3
Three clubs share funding. Initially A:B=5:6 and B:C=6:9. A then gives 31 of its own allocation to C; B keeps its allocation. C now has $374 more than A. How many dollars were allocated in total?
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Answer: 1020
- The linked ratio is 5:6:9.
- Write allocations as 5k,6k and 9k.
- After the transfer, C−A=(4+310)k=374
- k=51.
- Total funding is 20k=1020.