Why is 0.09B + B = 1.09B?

Question

In a question I was given, I was to try and find the value of B. In the second part of the question, a 9% sales tax was added to the value of B. I understand that my new equation would be B = B+0.09B.

 

Looking at the explanation of the question, I see that I was on the right track. However, instead of leaving it at 0.09B + B, 1.09B was given.

 

How did they arrive at this variable? Even if the information provided seems vague, can you at least please help me try to understand why a variable plus 0.09 times that variable is 1.09 of that variable?

Answer 1

If I have 2(4) + 3(4) it totals to (2+3)(4) = 5(4) = 20

Check:  2(4) + 3(4) = 8 + 12 = 20

 

If I have x apples then the quantity is understood

to be a single x or 1x.  We don't put a number in

front of the variable unless it is other than 1.

x + 2x = 3x

 

In this case here we have 1 of something and we

add .09 of that same thing to it giving 1.09 of that thing:

 

B + .09B = 1B + .09B = (1+.09)B = 1.09B

 

Understand?

 

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As to sales tax.  If I buy a $15 shirt and there is 6%

sales tax then my cost is 1(15) + .06(15) = (1.06)(15) =  $15.90

 

If the shirt costs $B and there is sales tax of 9% then

my cost is  B + .09B = (1+.09)B = $1.09B