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 : 7 : 1. There are
34 as many large potatoes as medium potatoes. There are
13 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 |
| 12 u |
7 u |
1 u |
100 kg |
| Number of potatoes |
| Large |
Medium |
Small |
| 3 |
4 |
|
| 3 |
|
1 |
| 3 p |
4 p |
1 p |
Total mass of potatoes
= 12 u + 7 u + 1 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 4
= 240
3 p = 240
1 p = 240 ÷ 3 = 80
Total number of small and medium potatoes
= 4 p + 1 p
= 5 p
= 5 x 80
= 400
Answer(s): 400
