154 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 : 3. There are
78 as many large potatoes as medium potatoes. There are
57 as many small potatoes as large potatoes. There are 2 large potatoes per kilogram. Find the total number of small and medium potatoes.
| Mass of potatoes |
| Large |
Medium |
Small |
Total |
| 12 u |
7 u |
3 u |
154 kg |
| Number of potatoes |
| Large |
Medium |
Small |
| 7 |
8 |
|
| 7 |
|
5 |
| 7 p |
8 p |
5 p |
Total mass of potatoes
= 12 u + 7 u + 3 u
= 22 u
22 u = 154
1 u = 154 ÷ 22 = 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 2
= 168
7 p = 168
1 p = 168 ÷ 7 = 24
Total number of small and medium potatoes
= 8 p + 5 p
= 13 p
= 13 x 24
= 312
Answer(s): 312
