162 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 : 7 : 1. There are
34 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 |
10 u |
7 u |
1 u |
162 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
4 |
|
3 |
|
2 |
3 p |
4 p |
2 p |
Total mass of potatoes
= 10 u + 7 u + 1 u
= 18 u
18 u = 162
1 u = 162 ÷ 18 = 9
Mass of large potatoes
= 10 u
= 10 x 9
= 90 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 90 x 2
= 180
3 p = 180
1 p = 180 ÷ 3 = 60
Total number of small and medium potatoes
= 4 p + 2 p
= 6 p
= 6 x 60
= 360
Answer(s): 360