75 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 : 4 : 1. There are
58 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 |
4 u |
1 u |
75 kg |
Number of potatoes |
Large |
Medium |
Small |
5 |
8 |
|
5 |
|
4 |
5 p |
8 p |
4 p |
Total mass of potatoes
= 10 u + 4 u + 1 u
= 15 u
15 u = 75
1 u = 75 ÷ 15 = 5
Mass of large potatoes
= 10 u
= 10 x 5
= 50 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 50 x 3
= 150
5 p = 150
1 p = 150 ÷ 5 = 30
Total number of small and medium potatoes
= 8 p + 4 p
= 12 p
= 12 x 30
= 360
Answer(s): 360