126 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 : 1. There are
519 as many large potatoes as medium potatoes. There are
35 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 |
7 u |
1 u |
126 kg |
Number of potatoes |
Large |
Medium |
Small |
5 |
19 |
|
5 |
|
3 |
5 p |
19 p |
3 p |
Total mass of potatoes
= 10 u + 7 u + 1 u
= 18 u
18 u = 126
1 u = 126 ÷ 18 = 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 3
= 210
5 p = 210
1 p = 210 ÷ 5 = 42
Total number of small and medium potatoes
= 19 p + 3 p
= 22 p
= 22 x 42
= 924
Answer(s): 924