180 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 : 1. There are
910 as many large potatoes as medium potatoes. There are
49 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 |
12 u |
7 u |
1 u |
180 kg |
Number of potatoes |
Large |
Medium |
Small |
9 |
10 |
|
9 |
|
4 |
9 p |
10 p |
4 p |
Total mass of potatoes
= 12 u + 7 u + 1 u
= 20 u
20 u = 180
1 u = 180 ÷ 20 = 9
Mass of large potatoes
= 12 u
= 12 x 9
= 108 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 108 x 4
= 432
9 p = 432
1 p = 432 ÷ 9 = 48
Total number of small and medium potatoes
= 10 p + 4 p
= 14 p
= 14 x 48
= 672
Answer(s): 672