135 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 : 1. There are
47 as many large potatoes as medium potatoes. There are
34 as many small potatoes as large potatoes. There are 3 large potatoes per kilogram. Find the total number of small and medium potatoes.
Mass of potatoes |
Large |
Medium |
Small |
Total |
8 u |
6 u |
1 u |
135 kg |
Number of potatoes |
Large |
Medium |
Small |
4 |
7 |
|
4 |
|
3 |
4 p |
7 p |
3 p |
Total mass of potatoes
= 8 u + 6 u + 1 u
= 15 u
15 u = 135
1 u = 135 ÷ 15 = 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 3
= 216
4 p = 216
1 p = 216 ÷ 4 = 54
Total number of small and medium potatoes
= 7 p + 3 p
= 10 p
= 10 x 54
= 540
Answer(s): 540