To Guest55 or mystery, what Year Gp is this question pitched

[Optimist]

Hi Guest55

I hope you are well.

I need your help, please, on a better explanation to the solution I gave to the following question.

Q.

Two stools and three chairs cost £1701. The cost of the chair is half the cost of the stool. Find the cost of a stool.

A.

Since one stool is double the cost of a chair, and assuming one chair is one unit then:

Chairs = 3 units
Stools = 4 units (2 chairs X 2 units)

So, 1701 divided by 7 units = £243

Cost of a stool = 2 X £243 = £486

NB, ds got confused that if chair is half the value of a stool, then stool is double the value of a chair

[Guest55]

Two stools and three chairs cost £1701.
The cost of the chair is half the cost of the stool.
Find the cost of a stool.

If that is the stumbling point then I'd ignore the £1 701 and say something like 'if we know the stool is £10, how much would the chair be?'

[Optimist]

Thank you Guest55. I spent time with him and mentioned that if A was 1/2 B, then B was twice A, C was 1/3 D then D was three times C, and so on.

This next one was equally difficult to explain. Again, is there a simpler method. Advice much appreciated.

Q.

Mark and David had the same amount of money. After Mark spent 48p at a shop, David had four times as much money as Mark. How much money did each of them have at first.

A.

I had to use a picture model and came up with 64 p each.

I stated David had 4 units (the "4 times").
Mark has one unit plus 48p.

therefore David's 4 units = Mark's one unit + 48 p.
so 48p = 3 units, so 1 unit = 16p

Therefore Mark has 16p + 48p = 64p at first.

To prove it, David had 4 X 16p = 64p at first.

[Guest55]

Mark and David had the same amount of money.
After Mark spent 48p at a shop, David had four times as much money as Mark.
How much money did each of them have at first.

Try getting him to make up similar questions then it might understand how to unpick them?

I think I would focus on getting some objects e.g. pennies, counters and trying out this sort of thing. So if we both had 20 counters and I spend 10 then ....

In the example above I can 'see' that 48p must be three quarters of the original but he won't get that immediately.

[moved]

Thank you Guest55. I spent time with him and mentioned that if A was 1/2 B, then B was twice A, C was 1/3 D then D was three times C, and so on.

This next one was equally difficult to explain. Again, is there a simpler method. Advice much appreciated.

Q.

Mark and David had the same amount of money. After Mark spent 48p at a shop, David had four times as much money as Mark. How much money did each of them have at first.

A.

I had to use a picture model and came up with 64 p each.

I stated David had 4 units (the "4 times").
Mark has one unit plus 48p.

therefore David's 4 units = Mark's one unit + 48 p.
so 48p = 3 units, so 1 unit = 16p

Therefore Mark has 16p + 48p = 64p at first.

To prove it, David had 4 X 16p = 64p at first.

I would teach teachers to teach it in exactly this way. A picture (bar) model.

[Optimist]

Dear Guest55

As promised, I have another difficult problem for you. I explained the answer to DS, however, I drew a model, and that scares him. Is there a simpler way, please.

A bottle of pop costs twice as much as a candy bar. If the cost of the candy bar is raised by £1.20 and the cost of the bottle of pop is lowered by £2.00, they would both cost the same amount.

1. Find the cost of the candy bar.
2. find the aggregated cost of the candy bar and the bottle of pop.

I drew a model, wrong idea I think. Using the drawing the cost difference is 2 units - 1 unit, which equals 1 unit

Therefore £1.20 + £2.00 = £3.20

1. So one bottle of pop costs £3.20

2. Aggregated cost (1+2) units = 3 units
= 3 @ £3.20 equals £9.60.

As I said, I think I complicated it. Is there a simpler way, please.

[Guest55]

I think your method sounds fine but maybe a bit sophisticated for some children to unpick.

Try some real numbers and so he can see why the 'bit' must be the sum of the two changes.

- - - - - - - - - - C + £1.20 |

- - - - - - - - - - - - - - - - - - - - - P
------------------------------| £2.00

Hard to draw on a PC but the vertical lines are the two new equal prices meant to be vertically above each other and the 'gap between the candy bar original price C and the old pop price P is the same as original cost C.

[Optimist]

Thanks Guest55. Have prepped more with real numbers. This question is too much for an 8/9 year old.

[Guest55]

The language is very strange - who says 'pop' and 'candy bar' - is it from an American book?

[Optimist]

The language is very strange - who says 'pop' and 'candy bar' - is it from an American book?

It's from an old list of loose leaf sheets, and from the UK.