85 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 9 : 7 : 1. There are
511 as many large potatoes as medium potatoes. There are
25 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 |
9 u |
7 u |
1 u |
85 kg |
Number of potatoes |
Large |
Medium |
Small |
5 |
11 |
|
5 |
|
2 |
5 p |
11 p |
2 p |
Total mass of potatoes
= 9 u + 7 u + 1 u
= 17 u
17 u = 85
1 u = 85 ÷ 17 = 5
Mass of large potatoes
= 9 u
= 9 x 5
= 45 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 45 x 4
= 180
5 p = 180
1 p = 180 ÷ 5 = 36
Total number of small and medium potatoes
= 11 p + 2 p
= 13 p
= 13 x 36
= 468
Answer(s): 468