64 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
23 as many large potatoes as medium potatoes. There are
12 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 |
1 u |
64 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 + 1 u
= 16 u
16 u = 64
1 u = 64 ÷ 16 = 4
Mass of large potatoes
= 8 u
= 8 x 4
= 32 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 32 x 2
= 64
2 p = 64
1 p = 64 ÷ 2 = 32
Total number of small and medium potatoes
= 3 p + 1 p
= 4 p
= 4 x 32
= 128
Answer(s): 128