91 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 : 4 : 1. There are
811 as many large potatoes as medium potatoes. There are
58 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 |
4 u |
1 u |
91 kg |
Number of potatoes |
Large |
Medium |
Small |
8 |
11 |
|
8 |
|
5 |
8 p |
11 p |
5 p |
Total mass of potatoes
= 8 u + 4 u + 1 u
= 13 u
13 u = 91
1 u = 91 ÷ 13 = 7
Mass of large potatoes
= 8 u
= 8 x 7
= 56 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 56 x 4
= 224
8 p = 224
1 p = 224 ÷ 8 = 28
Total number of small and medium potatoes
= 11 p + 5 p
= 16 p
= 16 x 28
= 448
Answer(s): 448