100 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 12 : 5 : 3. There are
56 as many large potatoes as medium potatoes. There are
45 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 |
12 u |
5 u |
3 u |
100 kg |
Number of potatoes |
Large |
Medium |
Small |
5 |
6 |
|
5 |
|
4 |
5 p |
6 p |
4 p |
Total mass of potatoes
= 12 u + 5 u + 3 u
= 20 u
20 u = 100
1 u = 100 ÷ 20 = 5
Mass of large potatoes
= 12 u
= 12 x 5
= 60 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 60 x 3
= 180
5 p = 180
1 p = 180 ÷ 5 = 36
Total number of small and medium potatoes
= 6 p + 4 p
= 10 p
= 10 x 36
= 360
Answer(s): 360