90 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 : 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 |
12 u |
5 u |
1 u |
90 kg |
Number of potatoes |
Large |
Medium |
Small |
2 |
3 |
|
2 |
|
1 |
2 p |
3 p |
1 p |
Total mass of potatoes
= 12 u + 5 u + 1 u
= 18 u
18 u = 90
1 u = 90 ÷ 18 = 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
2 p = 180
1 p = 180 ÷ 2 = 90
Total number of small and medium potatoes
= 3 p + 1 p
= 4 p
= 4 x 90
= 360
Answer(s): 360