51 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
59 as many large potatoes as medium potatoes. There are
45 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 |
10 u |
6 u |
1 u |
51 kg |
Number of potatoes |
Large |
Medium |
Small |
5 |
9 |
|
5 |
|
4 |
5 p |
9 p |
4 p |
Total mass of potatoes
= 10 u + 6 u + 1 u
= 17 u
17 u = 51
1 u = 51 ÷ 17 = 3
Mass of large potatoes
= 10 u
= 10 x 3
= 30 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 30 x 3
= 90
5 p = 90
1 p = 90 ÷ 5 = 18
Total number of small and medium potatoes
= 9 p + 4 p
= 13 p
= 13 x 18
= 234
Answer(s): 234