112 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 9 : 4 : 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 |
9 u |
4 u |
1 u |
112 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
4 |
|
3 |
|
2 |
3 p |
4 p |
2 p |
Total mass of potatoes
= 9 u + 4 u + 1 u
= 14 u
14 u = 112
1 u = 112 ÷ 14 = 8
Mass of large potatoes
= 9 u
= 9 x 8
= 72 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 72 x 2
= 144
3 p = 144
1 p = 144 ÷ 3 = 48
Total number of small and medium potatoes
= 4 p + 2 p
= 6 p
= 6 x 48
= 288
Answer(s): 288