104 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 : 4 : 1. There are
49 as many large potatoes as medium potatoes. There are
34 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 |
4 u |
1 u |
104 kg |
Number of potatoes |
Large |
Medium |
Small |
4 |
9 |
|
4 |
|
3 |
4 p |
9 p |
3 p |
Total mass of potatoes
= 8 u + 4 u + 1 u
= 13 u
13 u = 104
1 u = 104 ÷ 13 = 8
Mass of large potatoes
= 8 u
= 8 x 8
= 64 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 64 x 3
= 192
4 p = 192
1 p = 192 ÷ 4 = 48
Total number of small and medium potatoes
= 9 p + 3 p
= 12 p
= 12 x 48
= 576
Answer(s): 576