In Mr Tan's orchard, the number of papaya trees to the number of banana trees is 3 : 8. The number of banana trees to the number of mango trees is 4 : 5.
- Write the ratio of papaya trees to banana trees to mango trees in its simplest form.
- The orchard has 105 trees altogether. How many mango trees are there?
Need a hint?
Make the number of banana parts the same in both ratios before you combine them.
Worked answer
- (a) Banana trees are 8 units in the first ratio, but 4 units in the second ratio.
- Multiply banana : mango = 4 : 5 by 2 to get 8 : 10.
- Papaya : banana : mango = 3 : 8 : 10, which is already in simplest form.
- (b) Total parts = 3 + 8 + 10 = 21.
- One part = 105 ÷ 21 = 5 trees.
- Mango trees = 10 × 5 = 50.
Answer: 50 mango trees
The mistake this question tests
Habit
Simplest form in final fraction answers
Pupils write the second ratio as 4 : 5 without changing it, so banana does not match and the combined ratio is wrong, giving 3 : 4 : 5 or similar.
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