144 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 : 5 : 1. There are
411 as many large potatoes as medium potatoes. There are
34 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 |
5 u |
1 u |
144 kg |
Number of potatoes |
Large |
Medium |
Small |
4 |
11 |
|
4 |
|
3 |
4 p |
11 p |
3 p |
Total mass of potatoes
= 12 u + 5 u + 1 u
= 18 u
18 u = 144
1 u = 144 ÷ 18 = 8
Mass of large potatoes
= 12 u
= 12 x 8
= 96 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 96 x 2
= 192
4 p = 192
1 p = 192 ÷ 4 = 48
Total number of small and medium potatoes
= 11 p + 3 p
= 14 p
= 14 x 48
= 672
Answer(s): 672