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 Post subject: Simultaneous Equations QuestionsPosted: Tue May 22, 2018 7:29 am

Joined: Tue May 22, 2018 7:23 am
Posts: 59
Some of you may know the type.
EG.
Andrew paid £12 for 4 cups of coffee
and 4 cups of tea. 3 cups of coffee
cost as much as 2 cups of tea.
What was the total cost of 5 cups of
tea and 5 cups of coffee?.

Is there any good practice for this type of question online or in a book?

PS: I do know the answer and how to work it out
The total cost of 5 cups of coffee and 5 cups of tea was £15

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 Post subject: Re: Simultaneous Equations QuestionsPosted: Tue May 22, 2018 8:44 am

Joined: Fri Mar 10, 2017 4:06 pm
Posts: 579
I don't think you even need to know the second piece of information to work out the answer.

If 4c + 4t = 12

then c + t = 3.

So 5c + 5t = 15.

So in one sense its quite straightforward, but in another sense its a bit tricky because the question includes unnecessary information (that 3 cups of coffee costs the same as 2 cups of tea) and its natural to assume that you need to use this to work out the answer and to try and include it in your calculation.

Last edited by Surferfish on Tue May 22, 2018 8:49 am, edited 1 time in total.

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 Post subject: Re: Simultaneous Equations QuestionsPosted: Tue May 22, 2018 8:45 am

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 16127
Make them up? They need no algebra to find the answer ...

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 Post subject: Re: Simultaneous Equations QuestionsPosted: Tue May 22, 2018 8:50 am

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 16127
Surferfish wrote:
I don't think you even need to know the second piece of information to work out the answer.

If 4c + 4t = 12

then c + t = 3.

So 5c + 5t = 15.

Please don't use algebra for this type - it's not needed.

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 Post subject: Re: Simultaneous Equations QuestionsPosted: Tue May 22, 2018 8:55 am

Joined: Fri Mar 10, 2017 4:06 pm
Posts: 579
Guest55 wrote:
Surferfish wrote:
I don't think you even need to know the second piece of information to work out the answer.

If 4c + 4t = 12

then c + t = 3.

So 5c + 5t = 15.

Please don't use algebra for this type - it's not needed.

How would you work out the answer then?

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 Post subject: Re: Simultaneous Equations QuestionsPosted: Tue May 22, 2018 9:01 am

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 16127
You use your brain and note that the total of each item is the same.

"3 ice creams and 4 lollies cost £5

6 ice creams and 5 lollies cost £8.50

How much does it cost to buy an ice cream and a lolly?"

We can see we are buying 9 of each. This costs £13.50 so one of each costs £1.50.

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 Post subject: Re: Simultaneous Equations QuestionsPosted: Tue May 22, 2018 9:06 am

Joined: Sat Oct 08, 2011 1:25 pm
Posts: 2113
Guest55 wrote:
You use your brain and note that the total of each item is the same.

"3 ice creams and 4 lollies cost £5

6 ice creams and 5 lollies cost £8.50

How much does it cost to buy an ice cream and a lolly?"

We can see we are buying 9 of each. This costs £13.50 so one of each costs £1.50.

With the greatest of respect I think this confuses the OP. This is different to the question that was asked, because in the OP the cost of tea and coffee is not the same..

Edit.... though I do agree that it is quite simple arithmetic that tea plus coffee is £3 so no algebra is required.

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 Post subject: Re: Simultaneous Equations QuestionsPosted: Tue May 22, 2018 9:14 am

Joined: Fri Mar 10, 2017 4:06 pm
Posts: 579
Guest55 wrote:
You use your brain and note that the total of each item is the same.

"3 ice creams and 4 lollies cost £5

6 ice creams and 5 lollies cost £8.50

How much does it cost to buy an ice cream and a lolly?"

We can see we are buying 9 of each. This costs £13.50 so one of each costs £1.50.

But that is exactly the same as the way I did it.

The "algebra" is just a neat, shorthand way of writing down the thought process which you went through and described in English words.

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 Post subject: Re: Simultaneous Equations QuestionsPosted: Tue May 22, 2018 9:47 am

Joined: Sat Oct 08, 2011 1:25 pm
Posts: 2113
Surferfish wrote:
Guest55 wrote:
You use your brain and note that the total of each item is the same.

"3 ice creams and 4 lollies cost £5

6 ice creams and 5 lollies cost £8.50

How much does it cost to buy an ice cream and a lolly?"

We can see we are buying 9 of each. This costs £13.50 so one of each costs £1.50.

But that is exactly the same as the way I did it.

The "algebra" is just a neat, shorthand way of writing down the thought process which you went through and described in English words.

Perhaps G55 was referring to the OP which referenced simultaneous equations.

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 Post subject: Re: Simultaneous Equations QuestionsPosted: Tue May 22, 2018 9:50 am

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 16127
Surferfish wrote:
But that is exactly the same as the way I did it.

The "algebra" is just a neat, shorthand way of writing down the thought process which you went through and described in English words.

With respect, it is not - you introduced notation which was unnecessary and I'd mark it wrong as you did not define your variables.

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