57 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 11 : 7 : 1. There are
23 as many large potatoes as medium potatoes. There are
12 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 |
11 u |
7 u |
1 u |
57 kg |
Number of potatoes |
Large |
Medium |
Small |
2 |
3 |
|
2 |
|
1 |
2 p |
3 p |
1 p |
Total mass of potatoes
= 11 u + 7 u + 1 u
= 19 u
19 u = 57
1 u = 57 ÷ 19 = 3
Mass of large potatoes
= 11 u
= 11 x 3
= 33 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 33 x 2
= 66
2 p = 66
1 p = 66 ÷ 2 = 33
Total number of small and medium potatoes
= 3 p + 1 p
= 4 p
= 4 x 33
= 132
Answer(s): 132