34 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 10 : 6 : 1. There are
512 as many large potatoes as medium potatoes. There are
45 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 |
10 u |
6 u |
1 u |
34 kg |
Number of potatoes |
Large |
Medium |
Small |
5 |
12 |
|
5 |
|
4 |
5 p |
12 p |
4 p |
Total mass of potatoes
= 10 u + 6 u + 1 u
= 17 u
17 u = 34
1 u = 34 ÷ 17 = 2
Mass of large potatoes
= 10 u
= 10 x 2
= 20 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 20 x 4
= 80
5 p = 80
1 p = 80 ÷ 5 = 16
Total number of small and medium potatoes
= 12 p + 4 p
= 16 p
= 16 x 16
= 256
Answer(s): 256