48 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 : 6 : 1. There are
37 as many large potatoes as medium potatoes. There are
23 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 |
9 u |
6 u |
1 u |
48 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
7 |
|
3 |
|
2 |
3 p |
7 p |
2 p |
Total mass of potatoes
= 9 u + 6 u + 1 u
= 16 u
16 u = 48
1 u = 48 ÷ 16 = 3
Mass of large potatoes
= 9 u
= 9 x 3
= 27 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 27 x 3
= 81
3 p = 81
1 p = 81 ÷ 3 = 27
Total number of small and medium potatoes
= 7 p + 2 p
= 9 p
= 9 x 27
= 243
Answer(s): 243