119 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 9 : 7 : 1. There are ²₃ as many large potatoes as medium potatoes. There are ¹₂ as many small potatoes as large potatoes. There are 4 large potatoes per kilogram. Find the total number of small and medium potatoes.

Mass of potatoes
Large	Medium	Small	Total
9 u	7 u	1 u	119 kg

Number of potatoes
Large	Medium	Small
2	3
2		1
2 p	3 p	1 p

Total mass of potatoes
= 9 u + 7 u + 1 u
= 17 u

17 u = 119 

1 u = 119 ÷ 17 = 7 

Mass of large potatoes
= 9 u
= 9 x 7
= 63 kg

The number of large potatoes is repeated.  

Total number of large potatoes
= 63 x 4
= 252

2 p = 252

1 p = 252 ÷ 2 = 126

Total number of small and medium potatoes
= 3 p + 1 p
= 4 p
= 4 x 126
= 504

Answer(s): 504