Going backwards

Hello, and welcome to Myriora Maths! In a sale, a jumper has twenty per cent off, and now it costs forty-eight pounds. What was the price before the sale? This one is tricky. Let's see.

Twenty per cent off means the new price is eighty per cent of the old price. So forty-eight pounds is eighty per cent.

Eighty per cent is eight lots of ten per cent. So ten per cent is forty-eight divided by eight: six pounds.

A hundred per cent is ten lots of ten per cent. Ten times six pounds is sixty pounds. That was the old price!

Always check. Twenty per cent of sixty pounds is twelve pounds. Sixty take away twelve is forty-eight pounds. It works!

Let's try one together. After ten per cent off, a toy costs nine pounds. So nine pounds is ninety per cent. What was the old price? Say it out loud!

Ninety per cent is nine pounds, so ten per cent is one pound. A hundred per cent is ten pounds!

Here's a question that catches lots of people. After twenty per cent off, a jumper costs forty-eight pounds. Some people add twenty per cent of forty-eight back on, and get fifty-seven pounds sixty. But the twenty per cent was taken from the old price, not the new one. The old price was sixty pounds!

Your turn! After a twenty-five per cent increase, a ticket costs fifty pounds. What did it cost before? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! The new price is a hundred and twenty-five per cent. That's five lots of twenty-five per cent, so twenty-five per cent is ten pounds. A hundred per cent is four lots: forty pounds!

Quick review. First work out what percentage the new price is. Then find one part, like ten per cent. Build back up to a hundred per cent. And always check your answer. See you next time!