Question

Juanita is shopping online for a used MP3 Player. She can spend at least $50, but no more than$210. Shipping and handling will cost $10.20. If sales tax is 7%, what is Juanita's price range for MP3 players?

Solution

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Step 1

1 of 2

Let xx be price of an MP3 player.

The total cost in purchasing an MP3 player is:

x+$10.20+0.07xx+\$10.20+0.07x

or

1.07x+$10.201.07x+\$10.20

So, we can write the compound inequality:

$501.07x+$10.20$210\$50\leq 1.07x+\$10.20\leq \$210

Subtract $10.20\$10.20 from each member:

$39.801.07x$199.80\$39.80\leq 1.07x\leq \$199.80

Divide each member by 1.07:

$37.201.07x$186.73(1)\$37.20\leq 1.07x\leq \$186.73\color{white}\tag{1}

So, Juanita can spend between $37.20\$37.20 and $186.73\$186.73, inclusive.

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