80 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 8 : 7 : 1. There are
45 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 |
8 u |
7 u |
1 u |
80 kg |
Number of potatoes |
Large |
Medium |
Small |
4 |
5 |
|
4 |
|
3 |
4 p |
5 p |
3 p |
Total mass of potatoes
= 8 u + 7 u + 1 u
= 16 u
16 u = 80
1 u = 80 ÷ 16 = 5
Mass of large potatoes
= 8 u
= 8 x 5
= 40 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 40 x 2
= 80
4 p = 80
1 p = 80 ÷ 4 = 20
Total number of small and medium potatoes
= 5 p + 3 p
= 8 p
= 8 x 20
= 160
Answer(s): 160