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05 Jun 2026, 22:35
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76% (03:23) correct
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The pre-tax price of a sofa is the same in every state. In one state, the price of the sofa, including a \(p\)% sales tax, is $930. In a neighboring state, the price of the same sofa is $795, including a \(\frac{p}{4}\)% sales tax. What would be the price of the sofa in a state with a 15% sales tax?
A. $825.00
B. $843.75
C. $855.00
D. $862.50
E. $930.00
A. $825.00
B. $843.75
C. $855.00
D. $862.50
E. $930.00
08 Jun 2026, 20:21
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Let the pre-tax price of the sofa be x.
Then:
x(1 + p/100) = 930
x(1 + p/400) = 795
Divide the equations:
(1 + p/100) / (1 + p/400) = 930/795 = 62/53
Multiply through:
4(400 + p) = 62(400 + p)
53(400 + p) = 62(400 + p/?) ← easier to clear fractions directly:
Using
(100 + p)/(100 + p/4) = 62/53
53(100 + p) = 62(100 + p/4)
5300 + 53p = 6200 + 15.5p
37.5p = 900
p = 24
Now find the pre-tax price:
x(1.24) = 930
x = 750
Price with 15% sales tax:
750 × 1.15 = 862.5
Therefore, the price of the sofa in a state with a 15% sales tax is
D. $862.50.
Then:
x(1 + p/100) = 930
x(1 + p/400) = 795
Divide the equations:
(1 + p/100) / (1 + p/400) = 930/795 = 62/53
Multiply through:
4(400 + p) = 62(400 + p)
53(400 + p) = 62(400 + p/?) ← easier to clear fractions directly:
Using
(100 + p)/(100 + p/4) = 62/53
53(100 + p) = 62(100 + p/4)
5300 + 53p = 6200 + 15.5p
37.5p = 900
p = 24
Now find the pre-tax price:
x(1.24) = 930
x = 750
Price with 15% sales tax:
750 × 1.15 = 862.5
Therefore, the price of the sofa in a state with a 15% sales tax is
D. $862.50.
08 Jun 2026, 22:54
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I would solve by creating 2 equations and solving it then
Lets assume price of the sofa as x
eq 1 - x + px/100 = 930
eq 2 - x + px/400 = 795
Now solve the equations
100x + px = 93000
400x + px = 318000
further solve it and you get px = 18000
Therefore px/100 = 180
Now take eq 1 and substitute px/100 to get the price of sofa
x + 180 = 930, therefore x = 750 and now find 15% of 750 = 112.5, therefore the price of sofa with 15% tax = 862.50 Option D
Lets assume price of the sofa as x
eq 1 - x + px/100 = 930
eq 2 - x + px/400 = 795
Now solve the equations
100x + px = 93000
400x + px = 318000
further solve it and you get px = 18000
Therefore px/100 = 180
Now take eq 1 and substitute px/100 to get the price of sofa
x + 180 = 930, therefore x = 750 and now find 15% of 750 = 112.5, therefore the price of sofa with 15% tax = 862.50 Option D
