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 10 : 3 : 1. There are
47 as many large potatoes as medium potatoes. There are
34 as many small potatoes as large potatoes. There are 4 large potatoes per kilogram. Find the total number of small and medium potatoes.
Mass of potatoes |
Large |
Medium |
Small |
Total |
10 u |
3 u |
1 u |
84 kg |
Number of potatoes |
Large |
Medium |
Small |
4 |
7 |
|
4 |
|
3 |
4 p |
7 p |
3 p |
Total mass of potatoes
= 10 u + 3 u + 1 u
= 14 u
14 u = 84
1 u = 84 ÷ 14 = 6
Mass of large potatoes
= 10 u
= 10 x 6
= 60 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 60 x 4
= 240
4 p = 240
1 p = 240 ÷ 4 = 60
Total number of small and medium potatoes
= 7 p + 3 p
= 10 p
= 10 x 60
= 600
Answer(s): 600