Answer:
Weight of dried bananas = 34.75 kg
Weight of dried apricot = 15.25 kg
Step-by-step explanation:
Given that:
Cost of dried bananas = $4.59 per kg
Cost of dried apricots = $6.59 per kg
Total weight of mixture = 50 kg
Sales price of dried fruit = $5.20 per kg
To find:
The weight of each type of dry fruit = ?
Solution:
Let weight of dried bananas =
kg
Let weight of dried apricot =
kg
![x+y=50 ...... (1)](https://tex.z-dn.net/?f=x%2By%3D50%20......%20%281%29)
Total cost of dried bananas = Cost of dried bananas per kg multiplied by weight of dried bananas
Total cost of dried bananas = $4.59![x](https://tex.z-dn.net/?f=x)
Total cost of dried apricots = Cost of dried apricots per kg multiplied by weight of dried apricots
Total cost of dried apricots = $6.59![y](https://tex.z-dn.net/?f=y)
As per question statement,
Total cost of dry fruits = $5.20
50 = $260
![260 = 4.59x+6.59y......(2)](https://tex.z-dn.net/?f=260%20%3D%204.59x%2B6.59y......%282%29)
Using <em>substitution:</em>
By equation (1):
![x = 50-y](https://tex.z-dn.net/?f=x%20%3D%2050-y)
Putting in equation (2):
![260 = 4.59 (50-y)+6.59y\\\Rightarrow 2y = 260 - 229.5\\\Rightarrow y = 15.25\ kg](https://tex.z-dn.net/?f=260%20%3D%204.59%20%2850-y%29%2B6.59y%5C%5C%5CRightarrow%202y%20%3D%20260%20-%20229.5%5C%5C%5CRightarrow%20y%20%3D%2015.25%5C%20kg)
![x = 50 - 15.25\\\Rightarrow x = 34.75\ kg](https://tex.z-dn.net/?f=x%20%3D%2050%20-%2015.25%5C%5C%5CRightarrow%20x%20%3D%2034.75%5C%20kg)
Therefore, the answer is:
Weight of dried bananas = 34.75 kg
Weight of dried apricot = 15.25 kg