28 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 10 : 3 : 1. 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 |
| 10 u |
3 u |
1 u |
28 kg |
| Number of potatoes |
| Large |
Medium |
Small |
| 3 |
5 |
|
| 3 |
|
2 |
| 3 p |
5 p |
2 p |
Total mass of potatoes
= 10 u + 3 u + 1 u
= 14 u
14 u = 28
1 u = 28 ÷ 14 = 2
Mass of large potatoes
= 10 u
= 10 x 2
= 20 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 20 x 3
= 60
3 p = 60
1 p = 60 ÷ 3 = 20
Total number of small and medium potatoes
= 5 p + 2 p
= 7 p
= 7 x 20
= 140
Answer(s): 140
