200 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 10 : 7 : 3. 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 |
10 u |
7 u |
3 u |
200 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
4 |
|
3 |
|
2 |
3 p |
4 p |
2 p |
Total mass of potatoes
= 10 u + 7 u + 3 u
= 20 u
20 u = 200
1 u = 200 ÷ 20 = 10
Mass of large potatoes
= 10 u
= 10 x 10
= 100 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 100 x 3
= 300
3 p = 300
1 p = 300 ÷ 3 = 100
Total number of small and medium potatoes
= 4 p + 2 p
= 6 p
= 6 x 100
= 600
Answer(s): 600