56 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 9 : 4 : 1. There are
23 as many large potatoes as medium potatoes. There are
12 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 |
9 u |
4 u |
1 u |
56 kg |
Number of potatoes |
Large |
Medium |
Small |
2 |
3 |
|
2 |
|
1 |
2 p |
3 p |
1 p |
Total mass of potatoes
= 9 u + 4 u + 1 u
= 14 u
14 u = 56
1 u = 56 ÷ 14 = 4
Mass of large potatoes
= 9 u
= 9 x 4
= 36 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 36 x 3
= 108
2 p = 108
1 p = 108 ÷ 2 = 54
Total number of small and medium potatoes
= 3 p + 1 p
= 4 p
= 4 x 54
= 216
Answer(s): 216