# Save 30%, be 30% better off?

Posted by: Gary Ernest Davis on: February 22, 2011

A travel advertisement running, currently in the US, says you can save 30% on travel costs, and so be 30% better off.

Is that right?

To make it easier to think about, let’s think how much we would save if we got 50% off the price of something.

Suppose some item we wanted cost $100, and the salesperson said we would get 50% off. This means we would pay only$50 when we thought we might have to pay $100. So we could actually get 2 items for the$100 we originally intended to spend.

That is, we could get the 1 item we wanted, plus an extra 1 for the $100. This, to me, means we are 100% better off. #### What about 1/3 off? Now let’s hone in on that 30% off. Suppose we are offered 33% off the price of an item. That’s pretty close to $\frac{1}{3}$ off, so let’s pretend it is, in fact, $\frac{1}{3}$ off the price. Let’s suppose the item was going to cost$90.

Now, with the discount of $\frac{1}{3}$ it will only cost $60. That means we have saved half the cost of getting another one. In other words, if we were prepared to spend$180 we would not get just 2 items, as we would have thought before we heard about the $\frac{1}{3}$ discount: we would actually get $\frac{180}{60}=3$ items.

So whereas we thought we would get 2 items for $180 we will actually get 3 items. This means we are one-half – or 50% – better off than without the discount. So a $\frac{1}{3}$ discount makes us 50% better off. Because $\frac{1}{3}$ is close to 30%, we should suspect that a 30% discount is probably going to make us closer to 50% better off, than 30% better off. #### So how much better off are we after a 30% discount? What if an item costs$100 and we are given a 30% discount?

This means we only pay $70 for the item. So if we were to spend$700 we would get 10 items after the discount.

Bu before the discount $700 would have only bought us 7 items, at$100 each.

So we are $\frac{3}{7} \approx 0.43 = 43\%$ better off after the 30% discount.