Doing maths in your head!

We had a very bright child on our 11+ course today. He loved mathematics and worked very quickly through the course and then wanted more to do. He said that he loved solving problems.

We gave him this one:

I think of two numbers whose sum is 26.

Twice the first number plus three times the second number make 63.

Find the numbers.

He followed his own method of working this out – and it took him about four minutes.

His answers were correct. He explained how he had done the sum – but it was all in his head – with no working out. We have chatted about working out over the course – but he was simply irrepressible.

This is what we suggested:

Let x be the first number.

Let y be the second number.

So equation 1 becomes x + y = 26
And equation 2 becomes 2x + 3y = 63.

To solve
x + y = 26
2x + 3y = 63

Multiply equation 1 by 2:

2x + 2y = 52

Now take the equations way:

2x + 3y = 63
2x + 2y = 52
y = 11

Put y = 11 in the equation x = y = 26

x + 11 = 26

x = 15

Answer: The numbers are 15 and 11.

Easy if you know how. Pretty good for a ten year old to do in his head!