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An algebra problem to end the week : simultaneous equations

I thought I’d finish the week with a problem from my friends at ‘Quora’.. but then I found most of this weeks problems were difficult questions requiring University Maths! Yes I could follow (most) of it but it was all a little ‘off-piste’ for this diary, So here is a problem with can solve using Simultaneous equations

A word problem

So I have picked out a wordy problem that might look complicated at first sight, but we really just need to turn it into a couple of equations…  Let’s see

 

 

Lets call our numbers a and b – That’s always a good start with Algebra.

 

Let’s get some simultaneous equations

The first equation gives us the sum. So

a + b = 26.

With the second equation, we need to decide which is the larger number. It doesn’t matter which be choose. Let’s say a is larger.

a =  5 + 2b  (a has a value 5 more than twice b)

This is where we can solve the simultaneous equations. I’ll make a video on all the ways to do this soon, but for now I am going to solve these ‘by substitution’

I am going to substitute into the first equation the expression for a in the second. In the () you will see I have replaced ‘a’ with what a = in the second

(5 + 2b) + b = 26

We can together together terms

5 + 3b = 26

Take 5 from both sides

3b = 21

And from this see that b = 7. And so a = 19 (Twice b plus 5).

Check your answer with the other equation

As a final check 7 + 19 = 26

So there we have it the two numbers are 19 and 7

For more information on solving simultaneous equations, take a look at this More Help on simultaneous equations

 

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