# Question

Gordon had two crates containing both lemons and pears in each crate.

The ration of the number of lemons to that of pears in Crate A was 7:5.

The ration of the number of lemons to that of pears in Crate B was 3:1.

There was an equal number of fruits in each crate.

Gordon transferred 1/5 of the pears from Crate A to B.

He then threw away 84 lemons from Crate B.

The ration of the number of pears to that of lemons in Crate B then became 5:6.

What was the total number of fruits in both crates at first?

Thank you Siglapmath

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Before transfer —
Crate A
lemons : pears : total
7u : 5u : 12u

Crate B
lemons : pears : total
3 : 1 : 4
9u : 3u : 12u

After transfer —
Crate A —
lemons pears : total
7u : 4u : 11u

Crate B —
lemons : pears
(9u – 84) : 4u

4u x 6 = 24u ——- (9u – 84) x 5 = 45u – 420
45u – 24u = 21u ——- 420
1u ——- 420/21 = 20
12u + 12u = 24u ——- 24 x 20 = 480

Ans : 480 fruits.

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Hi zinmkw

Could you check if the last ratio should be 6:5 instead?

Hi Siglapmath

Its not 6:5, thanks.

Thank you Siglapmath

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 Lemon Pear Total Crate A 7u 5u 12u Crate B 9u 3u 12u A – 1/5 pears -> B (1u) B – threw 84 lemons Crate B (in the end) 9u – 84 4u

In the end, Lemon(B) : Pear(B) -> 6:5

6p = 9u – 84

30p = 45u – 420

5p = 4u

30p = 24u

45u – 420 = 24u

21u = 420

u = 20

Total number of fruits at first -> 24u = 480