133 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 : 7 : 2. There are
717 as many large potatoes as medium potatoes. There are
57 as many small potatoes as large potatoes. There are 4 large potatoes per kilogram. Find the total number of small and medium potatoes.
Mass of potatoes |
Large |
Medium |
Small |
Total |
10 u |
7 u |
2 u |
133 kg |
Number of potatoes |
Large |
Medium |
Small |
7 |
17 |
|
7 |
|
5 |
7 p |
17 p |
5 p |
Total mass of potatoes
= 10 u + 7 u + 2 u
= 19 u
19 u = 133
1 u = 133 ÷ 19 = 7
Mass of large potatoes
= 10 u
= 10 x 7
= 70 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 70 x 4
= 280
7 p = 280
1 p = 280 ÷ 7 = 40
Total number of small and medium potatoes
= 17 p + 5 p
= 22 p
= 22 x 40
= 880
Answer(s): 880