84 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 8 : 5 : 1. There are
38 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 |
8 u |
5 u |
1 u |
84 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
8 |
|
3 |
|
2 |
3 p |
8 p |
2 p |
Total mass of potatoes
= 8 u + 5 u + 1 u
= 14 u
14 u = 84
1 u = 84 ÷ 14 = 6
Mass of large potatoes
= 8 u
= 8 x 6
= 48 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 48 x 2
= 96
3 p = 96
1 p = 96 ÷ 3 = 32
Total number of small and medium potatoes
= 8 p + 2 p
= 10 p
= 10 x 32
= 320
Answer(s): 320