76 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 12 : 6 : 1. There are
310 as many large potatoes as medium potatoes. There are
23 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 |
12 u |
6 u |
1 u |
76 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
10 |
|
3 |
|
2 |
3 p |
10 p |
2 p |
Total mass of potatoes
= 12 u + 6 u + 1 u
= 19 u
19 u = 76
1 u = 76 ÷ 19 = 4
Mass of large potatoes
= 12 u
= 12 x 4
= 48 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 48 x 2
= 96
3 p = 96
1 p = 96 ÷ 3 = 32
Total number of small and medium potatoes
= 10 p + 2 p
= 12 p
= 12 x 32
= 384
Answer(s): 384