100 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 12 : 6 : 2. There are
35 as many large potatoes as medium potatoes. There are
23 as many small potatoes as large potatoes. There are 3 large potatoes per kilogram. Find the total number of small and medium potatoes.
| Mass of potatoes |
| Large |
Medium |
Small |
Total |
| 12 u |
6 u |
2 u |
100 kg |
| Number of potatoes |
| Large |
Medium |
Small |
| 3 |
5 |
|
| 3 |
|
2 |
| 3 p |
5 p |
2 p |
Total mass of potatoes
= 12 u + 6 u + 2 u
= 20 u
20 u = 100
1 u = 100 ÷ 20 = 5
Mass of large potatoes
= 12 u
= 12 x 5
= 60 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 60 x 3
= 180
3 p = 180
1 p = 180 ÷ 3 = 60
Total number of small and medium potatoes
= 5 p + 2 p
= 7 p
= 7 x 60
= 420
Answer(s): 420
