Flash Card Percents Question "dinner cost.."

[AbigailS228]

Dinner cost $230 including a 15% tip. How much was dinner without the tip?

I totally understand the way the GMAT did this problem, i.e.
230=x*115/100, x=price of dinner=200

However, why can't you also do this:
230*85/100=price of dinner=195.5

Why aren't these two methods interchangeable?

[RonPurewal]

Dinner cost $230 including a 15% tip. How much was dinner without the tip?

I totally understand the way the GMAT did this problem, i.e.
230=x*115/100, x=price of dinner=200

However, why can't you also do this:
230*85/100=price of dinner=195.5

Why aren't these two methods interchangeable?

In this problem, there's...
... a price before tip,
... a price after tip.

* Think about which one of these things you need to take 15% of.

* In your second approach, are you taking 15% of the right thing? Nope.

[AbigailS228]

I am still a little lost. Why can't you do it both ways? By doing 230*.85 or 230=x*1.15, aren't you getting the price BEFORE the tip both times?

Sorry, I don't know why this isn't resonating with me!

[RonPurewal]

I am still a little lost. Why can't you do it both ways? By doing 230*.85 or 230=x*1.15, aren't you getting the price BEFORE the tip both times?

Sorry, I don't know why this isn't resonating with me!

No. By doing 0.85 times 230, you're taking 15% off of 230.

In other words, you're subtracting 15% of the amount WITH the tip. Bad.

[RonPurewal]

General study principle: If you're having trouble "intuiting" something, consider the same thing with easier numbers.

E.g., an item costs $100.
If it's marked up by 50%, the price goes to $150.

You can't take 50% back off of that quantity-- you'd get $75, which is way way less than the original $100.
"The thing you need to take 50% of" is the original $100.

Hope that makes sense.

[AbigailS228]

Of course! Ah thank you so much. Totally makes sense now.

[RonPurewal]

Sure.