126 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 : 6 : 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 |
| 11 u |
6 u |
1 u |
126 kg |
| Number of potatoes |
| Large |
Medium |
Small |
| 2 |
3 |
|
| 2 |
|
1 |
| 2 p |
3 p |
1 p |
Total mass of potatoes
= 11 u + 6 u + 1 u
= 18 u
18 u = 126
1 u = 126 ÷ 18 = 7
Mass of large potatoes
= 11 u
= 11 x 7
= 77 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 77 x 4
= 308
2 p = 308
1 p = 308 ÷ 2 = 154
Total number of small and medium potatoes
= 3 p + 1 p
= 4 p
= 4 x 154
= 616
Answer(s): 616
