Two unknowns

Hello, and welcome to Myriora Maths! Two numbers add up to twenty. One is six more than the other. What are they? There are two unknowns here! Let's see two ways to find them.

Draw two bars. The bigger bar is the smaller bar, plus six. Together they make twenty. Take the six away: fourteen is left for two equal bars. Half of fourteen is seven. So the numbers are seven and thirteen.

Check both facts. Seven add thirteen is twenty. And thirteen is six more than seven. Both work!

Here's another kind. Two apples and a banana cost eighty pence. One apple and a banana cost fifty pence. Look at the difference: one apple. So one apple costs thirty pence. Then the banana is fifty take away thirty: twenty pence.

With letters, call the numbers a and b. a add b is twenty, and a take away b is six. Add the two together, and the b's cancel: two a is twenty-six. So a is thirteen, and b is seven.

Let's try one together. Two numbers add up to fifteen. One is three more than the other. What are they? Say it out loud!

Fifteen take away three is twelve. Half of twelve is six. So the numbers are six and nine!

Here's a question that catches lots of people. Two numbers add up to twenty, and one is six more than the other. Some people say fourteen and six. They add up to twenty. But fourteen is eight more than six, not six more! The answer is thirteen and seven.

Your turn! A pen and a ruler cost seventy pence. Two pens and a ruler cost one pound. How much is the ruler? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! The difference is one pen, which costs thirty pence. So the ruler is seventy take away thirty: forty pence!

Quick review. When you have two unknowns, you need two facts. For a sum and a difference, take the difference away and halve. For pictures, look at what's different between the two. Always check both facts. See you next time!