153 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
619 as many large potatoes as medium potatoes. There are
56 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 |
12 u |
4 u |
1 u |
153 kg |
Number of potatoes |
Large |
Medium |
Small |
6 |
19 |
|
6 |
|
5 |
6 p |
19 p |
5 p |
Total mass of potatoes
= 12 u + 4 u + 1 u
= 17 u
17 u = 153
1 u = 153 ÷ 17 = 9
Mass of large potatoes
= 12 u
= 12 x 9
= 108 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 108 x 4
= 432
6 p = 432
1 p = 432 ÷ 6 = 72
Total number of small and medium potatoes
= 19 p + 5 p
= 24 p
= 24 x 72
= 1728
Answer(s): 1728