170 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
59 as many large potatoes as medium potatoes. There are
35 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 |
2 u |
170 kg |
Number of potatoes |
Large |
Medium |
Small |
5 |
9 |
|
5 |
|
3 |
5 p |
9 p |
3 p |
Total mass of potatoes
= 8 u + 7 u + 2 u
= 17 u
17 u = 170
1 u = 170 ÷ 17 = 10
Mass of large potatoes
= 8 u
= 8 x 10
= 80 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 80 x 2
= 160
5 p = 160
1 p = 160 ÷ 5 = 32
Total number of small and medium potatoes
= 9 p + 3 p
= 12 p
= 12 x 32
= 384
Answer(s): 384