Find the inverse of the function g(x)=2x+5 algebraically.
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Let m and j be the current ages of Matthew and Jenny, respectively.
Now, Matthew is 3 times as old as Jenny, so the variables are in the following relation:
In 7 years, both of them will be 7 years older, i.e. their ages will be m+7 and j+7, and Matthew will be twice as old:
Now, remembering that m=3j, we can rewrite the second equation as
So, Jenny is 7 and Matthew is 21 (he's 3 times older).
In fact, in 7 years, they will be 14 and 28, and Matthew will be twice as old.
The best buy is from dealership B because dealership B has a lesser base price
<h3>The add-on options</h3>For the purpose of this exercise, the add-on options to select are:
- Sunroof
- Keyless entry
The total amount of the add-on options is:
Total = $500 + $1500
Total = $2000
<u>The inequality</u>
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000
<u>Solve for x</u>
We have:
(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 17248.44
Divide both sides by (1 + 6.75%)
x ≤ 16157.79
The solution means that the base price of the car cannot exceed $16157.78 for dealership A
<u>The graph of the possible base price</u>
See attachment
<h3>Dealership B</h3>The total amount of the add-on options is:
Total = $750 + $1000
Total = $1750
<u>The inequality</u>
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000
<u>Solve for x</u>
We have:
(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 16725.28
Divide both sides by (1 + 6.75%)
x ≤ 15667.71
The solution means that the base price of the car cannot exceed $15667.71 for dealership B
<u>The graph of the possible base price</u>
See attachment
<h3>Where to buy from</h3>Buy from dealership B because dealership B has a lesser base price
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