The expression 0.07x+(x−300) models the final price of a television set with an instant rebate in a state that charges a sales tax. The sales tax is on the original price. Which expression represents the price of the television set after the instant rebate is applied but before the tax is applied?
Answers
Answer:
B.
x
−
300
Explanation:
Given:
0.07
x
+
(
x
−
300
)
In this expression:
x
is the original price of the television before rebate and tax.
300
is the instant rebate.
0.07
is the rate of sales tax,
7
%, since
7
100
=
0.07
.
We get the final price by subtracting the rebate, getting
(
x
−
300
)
, then adding the tax, which is
7
% of the original price, i.e.
7
100
⋅
x
=
0.07
x
.
Notice that:
0.07
x
+
(
x
−
300
)
=
0.07
x
+
x
−
300
0.07
x
+
(
x
−
300
)
=
(
0.07
+
1
)
x
−
300
0.07
x
+
(
x
−
300
)
=
1.07
x
−
300
So what does
1.07
x
represent here? It is the price of the television including tax, but not taking the rebate into account. So if the shop displays tax-inclusive prices, this would be the value on the price tag .
Looking at the possible answers, we find:
A.
1.07
x
×
×
x
The tax inclusive price, before rebate.
B.
(
x
−
300
)
×
The price after instant rebate, but before sales tax is added.
C.
0.07
x
−
300
x
The total adjustment applied to the original price.
D.
0.07
x
×
×
x
The sales tax applied, namely
7
%
=
7
100
of the original price
x
.