170 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 : 4 : 1. There are
56 as many large potatoes as medium potatoes. There are
35 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 |
12 u |
4 u |
1 u |
170 kg |
Number of potatoes |
Large |
Medium |
Small |
5 |
6 |
|
5 |
|
3 |
5 p |
6 p |
3 p |
Total mass of potatoes
= 12 u + 4 u + 1 u
= 17 u
17 u = 170
1 u = 170 ÷ 17 = 10
Mass of large potatoes
= 12 u
= 12 x 10
= 120 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 120 x 2
= 240
5 p = 240
1 p = 240 ÷ 5 = 48
Total number of small and medium potatoes
= 6 p + 3 p
= 9 p
= 9 x 48
= 432
Answer(s): 432