120 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
35 as many large potatoes as medium potatoes. There are
13 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 |
120 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
5 |
|
3 |
|
1 |
3 p |
5 p |
1 p |
Total mass of potatoes
= 8 u + 6 u + 1 u
= 15 u
15 u = 120
1 u = 120 ÷ 15 = 8
Mass of large potatoes
= 8 u
= 8 x 8
= 64 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 64 x 3
= 192
3 p = 192
1 p = 192 ÷ 3 = 64
Total number of small and medium potatoes
= 5 p + 1 p
= 6 p
= 6 x 64
= 384
Answer(s): 384