document.write( "Question 127232: This question must be solved using inequality. I have tried all night, but could not get it.\r
\n" ); document.write( "\n" ); document.write( "Ronald wants to sell his car through a broker who charges a commission of 10% of the selling price. Ronald still owes $11,025. He must get enough to at least pay off the loan. What is the range of the selling price. \n" ); document.write( "
Algebra.Com's Answer #93205 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Let's start by saying that the selling price is represented by P.
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\n" ); document.write( "Next, if the buyer pays P dollars for the car, what's the first thing that happens? The
\n" ); document.write( "broker takes 10% or one-tenth (0.1) of P as the charge for his work in selling the car. Ronald
\n" ); document.write( "then gets what's left. So P dollars is the selling price and after the broker takes 0.1P
\n" ); document.write( "as the cost of his work, then what's left is P minus 0.1P or 0.9P.
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\n" ); document.write( "Therefore, the money that Ronald has left to pay off the loan is 0.9P. And Ronald needs that
\n" ); document.write( "amount to be at least the amount he owes on the car. (If it were more than he still owes,
\n" ); document.write( "I'm sure that he'd like that very much because he could spend the rest or save it for a
\n" ); document.write( "\"rainy day.\"
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\n" ); document.write( "So writing this as an inequality of requiring 0.9P to be at least equal to or greater than
\n" ); document.write( "the amount owed we can say:
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\n" ); document.write( "0.9P ≥ $11025
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\n" ); document.write( "To solve this for P you simply divide both sides of this inequality by the multiplier of
\n" ); document.write( "P just as you would in an equation. The multiplier of P is 0.9, so divide both sides of the
\n" ); document.write( "inequality by 0.9 as follows:
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\n" ); document.write( "0.9P/0.9 ≥ $11025/0.9
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\n" ); document.write( "On the left side of the inequality the 0.9 in the numerator cancels with the 0.9 in the
\n" ); document.write( "denominator and you are left with just P. On the right side when you divide the $11025 in
\n" ); document.write( "the numerator by the 0.9 in the denominator, you get $12,250. This means that the problem
\n" ); document.write( "is reduced to:
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\n" ); document.write( "P ≥ $12,250
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\n" ); document.write( "This says that Ronald needs to have the broker sell the car for $12,250 or more in order
\n" ); document.write( "for there to be enough to give the broker 10% ($1225) for selling the car and to pay off
\n" ); document.write( "the $11,025 still owed on the loan. Note that $1225 + $11,025 does equal the selling price
\n" ); document.write( "that Ronald at least needs. If the broker sells the car for more that $12,250 what happens?
\n" ); document.write( "Say the broker sells it for $13,000. The broker takes 10% or $1,300 and gives the remaining
\n" ); document.write( "$11,700 to Ronald, and Ronald pays off his $11,025 loan from that amount. He has $11,700 minus $11,025
\n" ); document.write( "which is $675 left to use in whatever way he chooses.
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\n" ); document.write( "Hope this helps you to understand this inequality problem and how you can think your way through
\n" ); document.write( "to a solution.
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