68 kg of potatoes are sorted into 3 sizes: large, medium and small. The ratio by mass of the large to medium to small potatoes is 11 : 5 : 1. There are ⁸₉ as many large potatoes as medium potatoes. There are ⁵₈ as many small potatoes as large potatoes. There are 2 large potatoes per kilogram. Find the total number of small and medium potatoes.

Mass of potatoes
Large	Medium	Small	Total
11 u	5 u	1 u	68 kg

Number of potatoes
Large	Medium	Small
8	9
8		5
8 p	9 p	5 p

Total mass of potatoes
= 11 u + 5 u + 1 u
= 17 u

17 u = 68 

1 u = 68 ÷ 17 = 4 

Mass of large potatoes
= 11 u
= 11 x 4
= 44 kg

The number of large potatoes is repeated.  

Total number of large potatoes
= 44 x 2
= 88

8 p = 88

1 p = 88 ÷ 8 = 11

Total number of small and medium potatoes
= 9 p + 5 p
= 14 p
= 14 x 11
= 154

Answer(s): 154