38 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
49 as many large potatoes as medium potatoes. There are
34 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 |
10 u |
7 u |
2 u |
38 kg |
Number of potatoes |
Large |
Medium |
Small |
4 |
9 |
|
4 |
|
3 |
4 p |
9 p |
3 p |
Total mass of potatoes
= 10 u + 7 u + 2 u
= 19 u
19 u = 38
1 u = 38 ÷ 19 = 2
Mass of large potatoes
= 10 u
= 10 x 2
= 20 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 20 x 2
= 40
4 p = 40
1 p = 40 ÷ 4 = 10
Total number of small and medium potatoes
= 9 p + 3 p
= 12 p
= 12 x 10
= 120
Answer(s): 120