Larry has an oil painting that he bought for $700 and now wants to sell.How much more profit could he gain by fixing a 30% profit based on the selling price rather than a 30 % profit based on the cost?

.3 * 700 = $210 based on cost

What is the selling price?

SO, 700+210, correct?

To calculate the profit based on the selling price, we need to find out what price Larry would sell the painting for. Let's call this price "S".

If Larry wants to make a 30% profit based on the selling price, the selling price would be the cost price (the original price he bought the painting for), plus 30% of the selling price:
S = $700 + 30% of S

To solve for S, we can rewrite the equation as:
S - 0.30S = $700

Combining the terms on the left side, we have:
0.70S = $700

To isolate S, we divide both sides of the equation by 0.70:
S = $700 / 0.70
S ≈ $1000

So, Larry would sell the painting for approximately $1000.

Now, let's calculate the profit based on the cost price. A 30% profit based on the cost price means that Larry would sell the painting for the cost price plus 30% of the cost price.

If Larry bought the painting for $700, then the selling price based on the cost price would be:
Selling Price = $700 + 30% of $700

To calculate the amount of profit, we need to subtract the cost price from the selling price:
Profit = Selling Price - Cost Price

Substituting the values:
Profit = ($700 + 0.30 * $700) - $700

Evaluating the expression:
Profit = $700 + $210 - $700
Profit = $210

Therefore, Larry could gain an additional profit of $210 by fixing a 30% profit based on the selling price rather than a 30% profit based on the cost price.