140 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 : 5 : 1. There are
516 as many large potatoes as medium potatoes. There are
45 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 |
8 u |
5 u |
1 u |
140 kg |
Number of potatoes |
Large |
Medium |
Small |
5 |
16 |
|
5 |
|
4 |
5 p |
16 p |
4 p |
Total mass of potatoes
= 8 u + 5 u + 1 u
= 14 u
14 u = 140
1 u = 140 ÷ 14 = 10
Mass of large potatoes
= 8 u
= 8 x 10
= 80 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 80 x 2
= 160
5 p = 160
1 p = 160 ÷ 5 = 32
Total number of small and medium potatoes
= 16 p + 4 p
= 20 p
= 20 x 32
= 640
Answer(s): 640