A bird park had parrots and budgies in the ratio 3 : 8. The park sold 6 parrots and bought 20 more budgies. After this, the ratio of the number of parrots to the number of budgies became 1 : 4. How many birds were there altogether at first?
- 88
- 121
- 135
- 154
Need a hint?
Write the number of budgies as 4 times the number of parrots after the change, then solve for one part.
Worked answer
- Let one part be u. At first, parrots = 3u and budgies = 8u.
- After the change, parrots = 3u − 6 and budgies = 8u + 20.
- The ratio is now 1 : 4, so budgies = 4 × parrots: 8u + 20 = 4(3u − 6).
- 8u + 20 = 12u − 24, so 4u = 44 and u = 11.
- At first there were 3 × 11 = 33 parrots and 8 × 11 = 88 budgies, a total of 121 birds.
Answer: 121 birds
The mistake this question tests
Habit
Calculation slip
Many pupils find only the budgies at first (88) and stop, forgetting to add the parrots.
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