The function for the amount saved if they purchase a used drone rather than a new drone from Jim's store is f(x) = 0.45x
He sells used drones at 70% of the price (x).
So, the selling price of a used drone is:
[tex]\mathbf{Used = 70\% \times x}[/tex]
Express percentage as decimal
[tex]\mathbf{Used = 0.7 \times x}[/tex]
[tex]\mathbf{Used = 0.7x}[/tex]
Also, he sells new drones at 15% more of the price (x).
So, the selling price of a new drone is:
[tex]\mathbf{New= (1 + 15\%) \times x}[/tex]
Express percentage as decimal
[tex]\mathbf{New= (1 + 0.15) \times x}[/tex]
[tex]\mathbf{New= 1.15 \times x}[/tex]
[tex]\mathbf{New= 1.15x}[/tex]
The amount saved is the difference between the prices of the drones.
So, we have:
[tex]\mathbf{Saved =New - Old}[/tex]
This gives
[tex]\mathbf{Saved =1.15x- 0.7x}[/tex]
Subtract
[tex]\mathbf{Saved =0.45x}[/tex]
Express as a function
[tex]\mathbf{f(x) = 0.45x}[/tex]
Hence, the function for the amount saved is f(x) = 0.45x
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