Respuesta :
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 = [tex]x[/tex]
Let number of pounds of dried kiwi purchased be = [tex]y[/tex]
Total weight of dried fruits purchased = [tex]x+y[/tex]
So, we have a sum equation as:
[tex]x+y=10[/tex]
Total cost of dried fruits = $40.34
Cost of a pound of dried mango = $2.11
Cost of [tex]x[/tex] pounds of dried mango in dollars can be given as = [tex]2.11x[/tex]
Cost of a dried kiwi = $5.07
Cost of [tex]y[/tex] pounds of dried kiwi in dollars can be given as = [tex]5.07y[/tex]
Total cost of dried fruits in dollars = [tex]2.11x+5.07y[/tex]
So, we have a cost equation as:
[tex]2.11x+5.07y=40.34[/tex]
The system of equations is :
A) [tex]x+y=10[/tex]
B) [tex]2.11x+5.07y=40.34[/tex]
Solving by substitution.
Rearranging equation A, to solve for [tex]y[/tex] in terms of [tex]x[/tex]
Subtracting both sides by [tex]x[/tex]
[tex]x+y-x=10-x[/tex]
[tex]y=10-x[/tex]
Substituting value of [tex]y[/tex] we got from A into equation B.
[tex]2.11x+5.07(10-x)=40.34[/tex]
Using distribution.
[tex]2.11x+50.7-5.07x=40.34[/tex]
Simplifying.
[tex]-2.96x+50.7=40.34[/tex]
Subtracting both sides by 50.7.
[tex]-2.96x+50.7-50.7=40.34-50.7[/tex]
[tex]-2.96x=-10.36[/tex]
Dividing both sides by -2.96.
[tex]\frac{-2.96x}{-2.96}=\frac{-10.36}{-2.96}[/tex]
∴ [tex]x=3.5[/tex]
We can plugin [tex]x=3.5[/tex] in the rearranged equation A to get value of [tex]y[/tex]
[tex]y=10-3.5[/tex]
∴ [tex]y=6.5[/tex]
So, number of pounds of dried mangoes Chloe bought = 3.5
Number of pounds of dried kiwi Chloe bought bough = 6.5
