Cathy spent $54 on some mangosteens, lemons and persimmons in the ratio of 5 : 3 : 1. The number of mangosteens was ⁵₆ the number of lemons. The ratio of the number of persimmons to the number of lemons was 2 : 1. The mangosteens were sold at 2 for a dollar.

1. How many fruits did she buy altogether?
2. How much did each lemon cost?

Amount spent
Mangosteens	Lemons	Persimmons	Total
5 u	3 u	1 u	9 u

Total amount spent on fruits
= 5 u + 3 u + 1 u
= 9 u

9 u = 54

1 u = 54 ÷ 9 = 6

Amount that Cathy spent on mangosteens
= 5 u
= 5 x 6
= $30 

Total number of mangosteens that Cathy bought
= 30 x 2
= 60

Number of fruits bought
Mangosteens	Lemons	Persimmons
5x1	6x1
	1x6	2x6
5 p	6 p	12 p

The number of lemons bought is repeated.  Make the number of lemons the same.  LCM of 1 and 6 is 6.

5 p = 60

1 p = 60 ÷ 5 = 12

Total number of fruits that Cathy bought
= 5 p + 6 p + 12 p
= 23 p
= 23 x 12
= 276

(b)
Total number of lemons that Cathy bought
= 6 p
= 6 x 12
= 72

Total amount that Cathy paid for the lemons
= 3 u
= 3 x 6
= $18

Price of each lemon
= 18 ÷ 72
= $0.25 

Answer(s): (a) 276; (b) $0.25