152 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 10 : 6 : 3. There are
45 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 |
10 u |
6 u |
3 u |
152 kg |
Number of potatoes |
Large |
Medium |
Small |
4 |
5 |
|
4 |
|
3 |
4 p |
5 p |
3 p |
Total mass of potatoes
= 10 u + 6 u + 3 u
= 19 u
19 u = 152
1 u = 152 ÷ 19 = 8
Mass of large potatoes
= 10 u
= 10 x 8
= 80 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 80 x 3
= 240
4 p = 240
1 p = 240 ÷ 4 = 60
Total number of small and medium potatoes
= 5 p + 3 p
= 8 p
= 8 x 60
= 480
Answer(s): 480