133 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 : 1. There are
711 as many large potatoes as medium potatoes. There are
37 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 |
1 u |
133 kg |
| Number of potatoes |
| Large |
Medium |
Small |
| 7 |
11 |
|
| 7 |
|
3 |
| 7 p |
11 p |
3 p |
Total mass of potatoes
= 12 u + 6 u + 1 u
= 19 u
19 u = 133
1 u = 133 ÷ 19 = 7
Mass of large potatoes
= 12 u
= 12 x 7
= 84 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 84 x 3
= 252
7 p = 252
1 p = 252 ÷ 7 = 36
Total number of small and medium potatoes
= 11 p + 3 p
= 14 p
= 14 x 36
= 504
Answer(s): 504
