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 : 5 : 1. There are
35 as many large potatoes as medium potatoes. There are
23 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 |
5 u |
1 u |
180 kg |
Number of potatoes |
Large |
Medium |
Small |
3 |
5 |
|
3 |
|
2 |
3 p |
5 p |
2 p |
Total mass of potatoes
= 12 u + 5 u + 1 u
= 18 u
18 u = 180
1 u = 180 ÷ 18 = 10
Mass of large potatoes
= 12 u
= 12 x 10
= 120 kg
The number of large potatoes is repeated.
Total number of large potatoes
= 120 x 3
= 360
3 p = 360
1 p = 360 ÷ 3 = 120
Total number of small and medium potatoes
= 5 p + 2 p
= 7 p
= 7 x 120
= 840
Answer(s): 840