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Question 9
3 points
9) A sofa is selling for $796, but the store is offering a 31.25% discount.
A sales tax of 9.875% will be applied to the sales price. Write an
equation and use it to estimate the final price of the sofa.
Your answer:​

Respuesta :

opudodennis

Answer:

$601.29

Step-by-step explanation:

-Given that the item has a discount of 31.25% and that the sales tax is at 9.875%

Let c be the sale price, p the regular price and d the discount rate.

#The cost of the item, c before sales tax is:

[tex]c=p(1-d)[/tex]

#Now let [tex]C_t[/tex] be the sale price after taxation.

-The sales tax is added to the listed price to determine the final sale price:

[tex]C_t=c(1+t), t=sales \ tax, c=p(1-d)\\\\C_t=p(1-d)(1+t)[/tex]

We substitute our values in the sale's equation to calculate the final sofa price:

[tex]C_t=p(1-d)(1+t)\ ,t=0.09875,d=0.3125, p=796\\\\=796(1-0.3125)(1+0.09875)\\\\=601.29[/tex]

Hence, the final price of the sofa is $601.29

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