Solving a Tough Profit Math Problem 📐

Don't freak out when you see this question in the test.

Even though it's long, you have to read it.

And you have time to read as long as you understand what you're reading.

So making sure that you understand is never time wasted.

Jean sells scarves that she gets from a supplier for $18 a piece and sells each for 30.

I think I might write down, you know, a gross profit of 12.

Will I use this number?

Perhaps a new supplier offers to provide the product at a discount.

Her gross profit will increase by 20% if she buys the same quantity from the new supplier.

So that means instead of 12, she makes 20% more.

So what's 20% of 12?

That's going to be 2.4.

And if you're curious the way I do that is 12 multiplied by 20%, which is 2 over 10.

And that's 12 times 2, 24 divided by 10.

2.4.

Now, what they're asking is the percentage discount the new supplier is offering on her original cost is closest to which one of the following.

Now, because I made this analysis as I went along, and I didn't just wait, I have some numbers ready, so I'm going to read this again just to be sure I understand what they want.

So this discount, which we say is 2.4, if we express it as a percentage of her original cost, what would it be?

So what is the original cost?

It is $18.

So what is 2.4 as a percentage of 18?

So times 100%.

What I can try is break it down and estimate, or if I struggle, I can ask myself.

15% times 18 gives me one answer that is closest to 2.4.

But this seems kind of tedious.

So what I'm going to do is I'm going to simplify these numbers.

I'm going to say that 2.4 is 24 over 10, which is 6 times 4.

So 2.4 is 24 over 10,.

Which is 6 times 4 divided by 10.

And then why that is valuable is for the following reason.

18 is 6 times 3.

And then I have that 100% over there.

So I can divide out the 6 with the 6.

I'm left with 4 over 30.

And I'm going to try and make this as close as 100 as possible for an easy reference.

So I'm going to multiply the top and the bottom by 3 1/3 times 3 1/3.

And so what I'm going to have is on the bottom 100.

So that's a nice number to compare to.

And four times three is 12 and then times a third.

So that's almost going to be three 13, and that is 13%.

So the correct answer is 13%.

So breaking numbers down is really helpful to being precise with choosing answer choices that seem too similar.