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# A chocolaty problem

Should I be posting more ‘seasonal problems’  Ha  maybe….   I’m a bit of a scrooge  really,  try not tow think of Christmas until December reaches double figures in the date

But here is a problem posted in one of my Facebook groups which I thought I’d share with my diary Might be the way I think, but I automatically think of Algebra when I see this problem

There are two things that we don’t know,  the weight of the box and the weight of a chocolate.  OK, we have only been asked for the weight of the box, not a chocolate but the weight of each chocolate is there in the problem, and I always like to add extra, especially if its chocolate!

Let b be the weight of the box, c the weight of 1 chocolate

b + 8c = 280g  : Eq1
b + 5c = 199g  : Eq2

Subtract Eq 2 from Eq 1 gived

3c = 81g   – so c = 27g

So from Eq 2  b + 135g  so c = 64g

I always like to use the other equation as a check when solving simultaneous equations

64 + 8 x 27 + 280g  as required by the check

# Algebra…. The language of maths

This is a rather general post, but since I am about to start on Algebra subjects with one GCSE student, I’ve been giving some thought on how sto start on this subject

A lot of students don’t like algebra. It’s probably the first thing they study in Maths that doesn’t seem to relate to ‘real life’.

But actually it’s very useful to know some algebra if you are going to solve some real life problems.

Algebra is the language that maths is written in.

Let’s start by considering the most important thing about Algebra – We use letters when we don’t know what numbers are. Each letter ‘represents’ a number.

This can work in different ways.

In this first example, you can choose what the numbers are

Choose your own value for a, b and c.

 a = 2 b = 3 C= 6

Now, with your numbers for a, b and c…   work out

 a + b   =  5 b – c  = 3 2 x a =  4 a – b + c  = 7 a x b + c = 12 c ÷ a = 3

These are no right and wrong answers! The answers depend on what numbers you chose. It’s fun, but is it much use?

We can make this more useful by turning these bits of algebra into a formula. We do this by making them ‘equal’ something

For example

 d = a x b + c f = c ÷ a

You have already worked these out. They are the last two examples above.

Formulas ARE useful because we can work out things from real life.

d = s x t

What is d if s = 30 and t = 3 ?

[This is how we work out how far we can travel if s is our speed and t is how long our journey is]

In my next post I’ll show how we can ‘simplify expressions that have the same letter repeated.