80 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 8 : 7 : 1. There are
59 as many large potatoes as medium potatoes. There are
25 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 |
| 8 u |
7 u |
1 u |
80 kg |
| Number of potatoes |
| Large |
Medium |
Small |
| 5 |
9 |
|
| 5 |
|
2 |
| 5 p |
9 p |
2 p |
Total mass of potatoes
= 8 u + 7 u + 1 u
= 16 u
16 u = 80
1 u = 80 ÷ 16 = 5
Mass of large potatoes
= 8 u
= 8 x 5
= 40 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 40 x 3
= 120
5 p = 120
1 p = 120 ÷ 5 = 24
Total number of small and medium potatoes
= 9 p + 2 p
= 11 p
= 11 x 24
= 264
Answer(s): 264
