Question 127232
Let's start by saying that the selling price is represented by P.
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Next, if the buyer pays P dollars for the car, what's the first thing that happens? The 
broker takes 10% or one-tenth (0.1) of P as the charge for his work in selling the car. Ronald 
then gets what's left. So P dollars is the selling price and after the broker takes 0.1P
as the cost of his work, then what's left is P minus 0.1P or 0.9P.
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Therefore, the money that Ronald has left to pay off the loan is 0.9P. And Ronald needs that
amount to be at least the amount he owes on the car. (If it were more than he still owes,
I'm sure that he'd like that very much because he could spend the rest or save it for a 
"rainy day."
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So writing this as an inequality of requiring 0.9P to be at least equal to or greater than
the amount owed we can say:
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0.9P ≥ $11025
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To solve this for P you simply divide both sides of this inequality by the multiplier of
P just as you would in an equation. The multiplier of P is 0.9, so divide both sides of the
inequality by 0.9 as follows:
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0.9P/0.9 ≥ $11025/0.9
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On the left side of the inequality the 0.9 in the numerator cancels with the 0.9 in the 
denominator and you are left with just P. On the right side when you divide the $11025 in
the numerator by the 0.9 in the denominator, you get $12,250. This means that the problem
is reduced to:
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P ≥ $12,250
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This says that Ronald needs to have the broker sell the car for $12,250 or more in order
for there to be enough to give the broker 10% ($1225) for selling the car and to pay off
the $11,025 still owed on the loan. Note that $1225 + $11,025 does equal the selling price
that Ronald at least needs. If the broker sells the car for more that $12,250 what happens? 
Say the broker sells it for $13,000. The broker takes 10% or $1,300 and gives the remaining
$11,700 to Ronald, and Ronald pays off his $11,025 loan from that amount. He has $11,700 minus $11,025
which is $675 left to use in whatever way he chooses.
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Hope this helps you to understand this inequality problem and how you can think your way through
to a solution.
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