63 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
916 as many large potatoes as medium potatoes. There are
59 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 |
63 kg |
Number of potatoes |
Large |
Medium |
Small |
9 |
16 |
|
9 |
|
5 |
9 p |
16 p |
5 p |
Total mass of potatoes
= 12 u + 7 u + 2 u
= 21 u
21 u = 63
1 u = 63 ÷ 21 = 3
Mass of large potatoes
= 12 u
= 12 x 3
= 36 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 36 x 3
= 108
9 p = 108
1 p = 108 ÷ 9 = 12
Total number of small and medium potatoes
= 16 p + 5 p
= 21 p
= 21 x 12
= 252
Answer(s): 252