Five friends—Allison, Beth, Carol, Diane, and Evelyn— have identical calculators and are studying for a statistics exam. They se
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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 =
Let number of pounds of dried kiwi purchased be =
Total weight of dried fruits purchased =
So, we have a sum equation as:
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 =
Cost of a dried kiwi = $5.07
Cost of pounds of dried kiwi in dollars can be given as =
Total cost of dried fruits in dollars =
So, we have a cost equation as:
The system of equations is :
A)
B)
Solving by substitution.
Rearranging equation A, to solve for in terms of
Subtracting both sides by
Substituting value of we got from A into equation B.
Using distribution.
Simplifying.
Subtracting both sides by 50.7.
Dividing both sides by -2.96.
∴
We can plugin in the rearranged equation A to get value of
∴
So, number of pounds of dried mangoes Chloe bought = 3.5
Number of pounds of dried kiwi Chloe bought bough = 6.5
We factor the denominators
Factor x^2 - 16
x^2 - 4^2
We use a^2 - b^2 = (a+b)(a-b)
so x^2 - 4^2 = (x+4)(x-4)
Replace it in the given equation
Excluded values are the values that makes the denominator 0
we have (x-4) and (x+4) in the denominator
We set the denominator =0 and solve for x
x-4 =0
Add 4 on both sides
x= 4
x+4=0
subtract 4 onboth side
so x= -4
Excluded values are x=-4 and x=4