#### 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

Verified#### Step 1

1 of 2Let $x$ be price of an MP3 player.

The total cost in purchasing an MP3 player is:

$x+\$10.20+0.07x$

or

$1.07x+\$10.20$

So, we can write the compound inequality:

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

Subtract $\$10.20$ from each member:

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

Divide each member by 1.07:

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

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

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