Answer:
Number of pounds of dried mangoes Chloe bought = 3.5
Number of pounds of dried kiwi Chloe bought bough = 6.5
Step-by-step explanation:
Total number of pounds of dried fruit purchased = 10
Let number of pounds of dried mango purchased = ![x](https://tex.z-dn.net/?f=x)
Let number of pounds of dried kiwi purchased be = ![y](https://tex.z-dn.net/?f=y)
Total weight of dried fruits purchased = ![x+y](https://tex.z-dn.net/?f=x%2By)
So, we have a sum equation as:
![x+y=10](https://tex.z-dn.net/?f=x%2By%3D10)
Total cost of dried fruits = $40.34
Cost of a pound of dried mango = $2.11
Cost of
pounds of dried mango in dollars can be given as = ![2.11x](https://tex.z-dn.net/?f=2.11x)
Cost of a dried kiwi = $5.07
Cost of
pounds of dried kiwi in dollars can be given as = ![5.07y](https://tex.z-dn.net/?f=5.07y)
Total cost of dried fruits in dollars = ![2.11x+5.07y](https://tex.z-dn.net/?f=2.11x%2B5.07y)
So, we have a cost equation as:
![2.11x+5.07y=40.34](https://tex.z-dn.net/?f=2.11x%2B5.07y%3D40.34)
The system of equations is :
A) ![x+y=10](https://tex.z-dn.net/?f=x%2By%3D10)
B) ![2.11x+5.07y=40.34](https://tex.z-dn.net/?f=2.11x%2B5.07y%3D40.34)
Solving by substitution.
Rearranging equation A, to solve for
in terms of ![x](https://tex.z-dn.net/?f=x)
Subtracting both sides by ![x](https://tex.z-dn.net/?f=x)
![x+y-x=10-x](https://tex.z-dn.net/?f=x%2By-x%3D10-x)
![y=10-x](https://tex.z-dn.net/?f=y%3D10-x)
Substituting value of
we got from A into equation B.
![2.11x+5.07(10-x)=40.34](https://tex.z-dn.net/?f=2.11x%2B5.07%2810-x%29%3D40.34)
Using distribution.
![2.11x+50.7-5.07x=40.34](https://tex.z-dn.net/?f=2.11x%2B50.7-5.07x%3D40.34)
Simplifying.
![-2.96x+50.7=40.34](https://tex.z-dn.net/?f=-2.96x%2B50.7%3D40.34)
Subtracting both sides by 50.7.
![-2.96x+50.7-50.7=40.34-50.7](https://tex.z-dn.net/?f=-2.96x%2B50.7-50.7%3D40.34-50.7)
![-2.96x=-10.36](https://tex.z-dn.net/?f=-2.96x%3D-10.36)
Dividing both sides by -2.96.
![\frac{-2.96x}{-2.96}=\frac{-10.36}{-2.96}](https://tex.z-dn.net/?f=%5Cfrac%7B-2.96x%7D%7B-2.96%7D%3D%5Cfrac%7B-10.36%7D%7B-2.96%7D)
∴ ![x=3.5](https://tex.z-dn.net/?f=x%3D3.5)
We can plugin
in the rearranged equation A to get value of ![y](https://tex.z-dn.net/?f=y)
![y=10-3.5](https://tex.z-dn.net/?f=y%3D10-3.5)
∴ ![y=6.5](https://tex.z-dn.net/?f=y%3D6.5)
So, number of pounds of dried mangoes Chloe bought = 3.5
Number of pounds of dried kiwi Chloe bought bough = 6.5