102 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 : 2. There are
23 as many large potatoes as medium potatoes. There are
12 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 |
2 u |
102 kg |
Number of potatoes |
Large |
Medium |
Small |
2 |
3 |
|
2 |
|
1 |
2 p |
3 p |
1 p |
Total mass of potatoes
= 8 u + 7 u + 2 u
= 17 u
17 u = 102
1 u = 102 ÷ 17 = 6
Mass of large potatoes
= 8 u
= 8 x 6
= 48 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 48 x 3
= 144
2 p = 144
1 p = 144 ÷ 2 = 72
Total number of small and medium potatoes
= 3 p + 1 p
= 4 p
= 4 x 72
= 288
Answer(s): 288