SOLUTION: The Smiths have saved $25,000 toward the purchase of a new car. If the sales tax is 5%, the purchase of the Smiths' new car before taxes cannot exceed what? I know the equation

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Question 1209250: The Smiths have saved $25,000 toward the purchase of a new car. If the sales tax is 5%, the purchase of the Smiths' new car before taxes cannot exceed what?
I know the equation is 1.05p< 25,000. What I do not understand is why is the amount 1.05 and not just 0.05 for the 5%.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.

"p" is the price of the car before tax.


The 5% tax adds 0.05p to the total cost.


So, the total cost is  p + 0.05p = (1+0.05)p = 1.05p.


To find "p", you should use this equation

    1.05p = 25000,


which gives you the solution for the affordable car price  before the tax

    p =  = 23810  dollars.

Solved, with explanations.   As clear as  1 + 2 = 3.   It couldn't be clearer.

Having this explanation,  please do not tell anymore
that you do not understand this type of problems/questions.



Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

p = price before tax
0.05p = tax
p+0.05p = 1.05p = price after tax

This final dollar amount can be $25,000 or less
It leads to the inequality

Divide both sides by 1.05 to arrive at the approximation which rounds to

The price before taxes cannot exceed $23,809.52
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