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The question is

A retailer sells widgets for $\$120$ each, which is $20\%$ more than they cost from wholesales. How much gross profit does the retailer earn after selling $8$ widgets

$\$ 140$

$\$ 148$

$\$ 160$

$\$ 172$

$\$ 176$

After some calculations, I get $\$192$ which in not in the answer list.

I dont know. Please correct me if I have just made a mistake in the middle.

Thanks

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Mind showing your calculations so we can see where you went astray? –  Joe Apr 21 '12 at 21:19
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2 Answers

up vote 1 down vote accepted

Let's first figure out what the retailer pays for a widget. Call this price $x$.

We're told that $120$ is twenty percent more that what the retailer paid for a widget. That is, $120$ is equal to $x$ plus twenty percent of $x$. Since twenty percent of $x$ is $.2x$, this gives us the equation $$120=x+0.2x,$$ or $$ 120=1.2x. $$ Solving this equation gives $x=100$ dollars.

So, the retailer pays 100 dollars for a widget and sells it for 120 dollars; thus the retailer makes a twenty dollar profit for each widget sold.

So if he sells eight widgets, then his total profit is...

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Let $x$ denote the profit of one widget. We can write an equation to find this:

$$(120-x)(1+.2) = 120$$ $$(120-x)(1.2) = 120$$ $$120 - x = 100$$ $$-x = -20$$ $$x = 20$$

Since we want to know how much the retailer makes for $8$ widgets, we can simply say that his net profit is $8x$ which would be $8(20)$ = $\$160$.

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