Daniel buys a desk that regularly sells for $250 and a desk chair that regularly sells for $145. Both items are on sale at 15% off, and a sales tax of x% is applied to both. Which expression does not represent the amount Daniel pays?

A. (395)(0.0085x)+395(0.85)
B.(0.85+x/100)(250+145)
C. 335.75+3.3575
D.(250+145)(1-0.15)(100+×/100)

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eurydike eurydike · Answer 1 · 2018-07-31T04:15:36+02:00

Daniel bought a desk which regularly costs $250. It is on sale that is 15% off.

In decimal 15% = 15/100 = 0.15

So after sale the selling price is $ (250 ×(1-0.15))

Also x% sales tax applied to it.

After including sales tax, the price is $(250 ×(1-0.15)) + $ (250 ×(1-0.15)×(x/100))

Now here $(250×(1-0.15) is common to both of them. If we take it out we will get $(250×(1-0.15)×(1+x/100))

So Daniel pays $(250×(1-0.15)×(1+x/100)) for a desk.

Daniel also bought a desk chair whose regular selling price is $145. There is 15% off.

So the price will be $(145 ×(1-0.15))

There is also x% sales tax. So after sales tax Daniel pays

$(145×(1-0.15)) + $(145×(1-0.15)×(x/100)

= $(145×(1-0.15)×(1+x/100))

So the total amount Daniel pays

$(250×(1-0.15)×(1+x/100)) + $(145×(1-0.15)×(1+x/100))

We can take out (1-0.15)×(1+x/100)

$(250+145)×(1-0.15)×(1+x/100) = $(250+145)×(1-0.15)×(100/100 + x/100)

=$(250+145)×(1-0.15)×((100+x)/100)

This is option D. So option D is correct.

$(250+145)×(1-0.15)×(1+x/100)

$395×(0.85)×(1+x/100)

$395×(0.85 + 0.85x/100)

$395×(0.85 + 0.0085x)

$395(0.85) + $395 (0.0085x)

This is option A. So option A is also correct.

We will not get option B and C. So we can say option B and C do not represent the amount that Daniel pays.