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 8 : 7 : 1. There are
310 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 |
8 u |
7 u |
1 u |
48 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
10 |
|
3 |
|
2 |
3 p |
10 p |
2 p |
Total mass of potatoes
= 8 u + 7 u + 1 u
= 16 u
16 u = 48
1 u = 48 ÷ 16 = 3
Mass of large potatoes
= 8 u
= 8 x 3
= 24 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 24 x 3
= 72
3 p = 72
1 p = 72 ÷ 3 = 24
Total number of small and medium potatoes
= 10 p + 2 p
= 12 p
= 12 x 24
= 288
Answer(s): 288