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 8 : 6 : 2. There are
34 as many large potatoes as medium potatoes. There are
23 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 |
8 u |
6 u |
2 u |
144 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
4 |
|
3 |
|
2 |
3 p |
4 p |
2 p |
Total mass of potatoes
= 8 u + 6 u + 2 u
= 16 u
16 u = 144
1 u = 144 ÷ 16 = 9
Mass of large potatoes
= 8 u
= 8 x 9
= 72 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 72 x 4
= 288
3 p = 288
1 p = 288 ÷ 3 = 96
Total number of small and medium potatoes
= 4 p + 2 p
= 6 p
= 6 x 96
= 576
Answer(s): 576