114 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 : 6 : 2. There are
35 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 |
11 u |
6 u |
2 u |
114 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
5 |
|
3 |
|
2 |
3 p |
5 p |
2 p |
Total mass of potatoes
= 11 u + 6 u + 2 u
= 19 u
19 u = 114
1 u = 114 ÷ 19 = 6
Mass of large potatoes
= 11 u
= 11 x 6
= 66 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 66 x 3
= 198
3 p = 198
1 p = 198 ÷ 3 = 66
Total number of small and medium potatoes
= 5 p + 2 p
= 7 p
= 7 x 66
= 462
Answer(s): 462