Help with question from the Manhattan Gmat flash cards #20

[rich0504]

Question #20 on the manhattan gmat flash cards. Carla earns a base salary of 30,000 plus 10% commission.........

I am stuck on the solution. The answer states that c= 0.1(r-50,000) which i get.

But from the statement: "if her total sales revenue had been 25% higher, her commission would have been 20% higher.

Then you guys rephrased that statement to read:
1.2c= 0.1(1.25r-50,000)

Where dose the 1.2c come from? Also where do you get 1.25r?

Please help...

[mschwrtz]

Where dose the 1.2c come from?

1.2c=120%c=her commission if it had 20% greater

Also where do you get 1.25r?

1.25r=125%r=her sales revenue if it had been 25% greater

[AbigailS228]

I am having trouble understanding how you can even derive the equation c=.1(r-50,000). Wouldn't it be -30,000?

I don't know why this is messing with me, I know it's a simple question but I am a little lost.

Thanks!

[RonPurewal]

The problem is that only half of the question is actually here.

Presumably, the question said something like "The commission is paid on all sales above $50,000". Hence subtracting out the first $50,000 from the revenue figure.

It wouldn't make any sense to put the $30,000 in that place, because $30,000 is not a revenue figure.
In other words, the expression (r - 30,000) would be a nonsense expression, since there's no sensible reason to subtract a base salary from someone's sales figures. (This would be like, say, adding my height and my weight.)

If the original poster had actually followed the forum rules and posted the entire problem, then we wouldn't be having this issue. Grr.

[AbigailS228]

This is the original problem:

Is the statement sufficient?

Carla earns a base salary of $30,000 plus 10% commission on her total sales revenue exceeding $50,00. How much did she make on commission this year?

1) If her total sales revenue had been 25% higher her commission would have been 20% higher

[RonPurewal]

So now you know where the 50,000 comes from. Do you have other questions/issues?

[AbigailS228]

I understand where the 50,000 came from, but I don't understand the logic of why we applied it here.

To further explain, I were to make the equations myself I would have just done c=.1r and then 1.2c=.1(1.25r). I just don't understand why you subtract the 50,000, because wouldn't the figure calculated not include 50,000 in it then (that is if we wanted to solve for Revenue and not Commission)? It doesn't ask for the Revenue without the 50,000 in it?

I hope my question makes better sense now.

Thanks

[RonPurewal]

The commission is paid only on the amount of sales above $50,000.

So, the commission is zero for sales ≤ 50,000. For values of sales > 50,000, it's 0.1(sales – 50,000).

Do you understand the subtraction? That's how we account for "sales above 50,000".
It might look weird in a formula, but I'm betting you'd just subtract instinctively if you were to encounter the same situation with concrete numbers in real life. (E.g., if you had to pay customs duty on "the value over $500" of something that cost $700, I don't think it would take you very long to realize that you'd have to pay customs duty on $200.)

The point is that, if "___" is the sales revenue, then the commission is 0.1(___ – 50,000).
In a hypothetical scenario in which the sales revenue is 1.25R, you just put 1.25R in the blank. The way in which the commission is computed does not change, so nothing else about the formula will be any different.

[AbigailS228]

Oh I see now. I didn't fully understand the question before. Thanks so much!

[tim]

:)

[RonPurewal]

Oh I see now. I didn't fully understand the question before. Thanks so much!

When you look at formulas, remember: Never think of the variables in the formula as variables. Instead, think of them as "places where you put stuff".
The "stuff" is often a larger expression (rather than just 1 variable or 1 number). In such cases, this way of thinking will make your life a lot easier.

[MarthaM266]

At the bottom, it offers for extra practice, what is the value of c and r?

How would we solve that?

Thanks!

[tim]

This is a system of two linearly independent equations with two variables. Try using the standard equation solving techniques you learned in high school algebra, and if you get stuck, let us know where you got stuck so we can help you from that point.

[CharlesG754]

I'm stuck... I calculate r = -200,000 and thus c = -25,000. And obviously negative numbers should be impossible?

The statement doesn't make sense to me. Carla earns 10% on total sales revenue (>$50k). So it should be a linear relationship, right? If sales revenue increases 25%, shouldn't her commission increase 25%? Am I missing something?

[RonPurewal]

I just don't understand why you subtract the 50,000, because wouldn't the figure calculated not include 50,000 in it then

the blue thing is exactly what SHOULD happen here.

the point, here, is that no commission is paid at all until you hit $50,000 in sales. AFTER that, a commission of %10 is paid ON THE AMOUNT EXCEEDING $50,000.

as is the case with most formulas, it's easier to understand with specific values. if you have $90,000 in sales, then your commission is 10 percent of 40,000 (NOT 10 percent of 90,000). then that amount is added to the base salary.

you're correct that we 'don't include the 50,000', in other words, because that's the whole point.