210 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 : 7 : 2. There are
23 as many large potatoes as medium potatoes. There are
12 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 |
12 u |
7 u |
2 u |
210 kg |
Number of potatoes |
Large |
Medium |
Small |
2 |
3 |
|
2 |
|
1 |
2 p |
3 p |
1 p |
Total mass of potatoes
= 12 u + 7 u + 2 u
= 21 u
21 u = 210
1 u = 210 ÷ 21 = 10
Mass of large potatoes
= 12 u
= 12 x 10
= 120 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 120 x 3
= 360
2 p = 360
1 p = 360 ÷ 2 = 180
Total number of small and medium potatoes
= 3 p + 1 p
= 4 p
= 4 x 180
= 720
Answer(s): 720