54 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 11 : 5 : 2. There are
34 as many large potatoes as medium potatoes. There are
23 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 |
11 u |
5 u |
2 u |
54 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
4 |
|
3 |
|
2 |
3 p |
4 p |
2 p |
Total mass of potatoes
= 11 u + 5 u + 2 u
= 18 u
18 u = 54
1 u = 54 ÷ 18 = 3
Mass of large potatoes
= 11 u
= 11 x 3
= 33 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 33 x 2
= 66
3 p = 66
1 p = 66 ÷ 3 = 22
Total number of small and medium potatoes
= 4 p + 2 p
= 6 p
= 6 x 22
= 132
Answer(s): 132