36 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 : 3. There are
45 as many large potatoes as medium potatoes. There are
34 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 |
8 u |
7 u |
3 u |
36 kg |
Number of potatoes |
Large |
Medium |
Small |
4 |
5 |
|
4 |
|
3 |
4 p |
5 p |
3 p |
Total mass of potatoes
= 8 u + 7 u + 3 u
= 18 u
18 u = 36
1 u = 36 ÷ 18 = 2
Mass of large potatoes
= 8 u
= 8 x 2
= 16 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 16 x 2
= 32
4 p = 32
1 p = 32 ÷ 4 = 8
Total number of small and medium potatoes
= 5 p + 3 p
= 8 p
= 8 x 8
= 64
Answer(s): 64