114 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 12 : 6 : 1. There are
25 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 |
12 u |
6 u |
1 u |
114 kg |
Number of potatoes |
Large |
Medium |
Small |
2 |
5 |
|
2 |
|
1 |
2 p |
5 p |
1 p |
Total mass of potatoes
= 12 u + 6 u + 1 u
= 19 u
19 u = 114
1 u = 114 ÷ 19 = 6
Mass of large potatoes
= 12 u
= 12 x 6
= 72 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 72 x 2
= 144
2 p = 144
1 p = 144 ÷ 2 = 72
Total number of small and medium potatoes
= 5 p + 1 p
= 6 p
= 6 x 72
= 432
Answer(s): 432