136 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 : 2. There are
34 as many large potatoes as medium potatoes. There are
23 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 |
2 u |
136 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
4 |
|
3 |
|
2 |
3 p |
4 p |
2 p |
Total mass of potatoes
= 8 u + 7 u + 2 u
= 17 u
17 u = 136
1 u = 136 ÷ 17 = 8
Mass of large potatoes
= 8 u
= 8 x 8
= 64 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 64 x 3
= 192
3 p = 192
1 p = 192 ÷ 3 = 64
Total number of small and medium potatoes
= 4 p + 2 p
= 6 p
= 6 x 64
= 384
Answer(s): 384