11 Plus Exams Forum

A bull and 3 cows costs £1300. Four bulls and 8 cows cost £4000. What is the cost of a bull.
How can I explain how to work this out to a 10 year old. Would it be best to use simple algebra? If so, how?
Thanks

A bull and 3 cows costs £1 300.
Four bulls and 8 cows cost £4 000.
What is the cost of a bull?

Personally I would avoid algebra unless you use b = no of bulls and c = no of cows.

Without algebra you can say from the first sentence that 4 bulls and 12 cows cost £5 200 so you can see how much 4 cows cost.

Then go from there - don't use x and y though.

for 10yr olds avoid formal algebra, it mostly arithmetic at this stage what I would call pre-algebra.
arithmetics is to maths what spelling is to writing.
Accelerated learning at that age just confuses young children in the long term.

Advanced children can explore algebra themselves using simple balance scales.

Formal algebra is not hard and can be taught to quite young children but requires expert help and unnecessary for all 11+ tests.

Guest55 wrote:

A bull and 3 cows costs £1 300.
Four bulls and 8 cows cost £4 000.
What is the cost of a bull?

Personally I would avoid algebra unless you use b = no of bulls and c = no of cows.

Without algebra you can say from the first sentence that 4 bulls and 12 cows cost £5 200 so you can see how much 4 cows cost.

Then go from there - don't use x and y though.

Isn't it 5 bulls and 11 cows cost £5300? Confused as to where 4 bulls and 12 cows cost £5200 came from?

pinkrabbit38 wrote:

Guest55 wrote:

A bull and 3 cows costs £1 300.
Four bulls and 8 cows cost £4 000.
What is the cost of a bull?

Personally I would avoid algebra unless you use b = no of bulls and c = no of cows.

Without algebra you can say from the first sentence that 4 bulls and 12 cows cost £5 200 so you can see how much 4 cows cost.

Then go from there - don't use x and y though.

Isn't it 5 bulls and 11 cows cost £5300? Confused as to where 4 bulls and 12 cows cost £5200 came from?

The '4 bulls and 12 cows' comes from multiplying the original '1 bull and 3 cows' by 4 so you can see the difference between that and the cost of the '4 bulls and 8 cows' the OP mentioned.

Where does the '5 bulls and 11 cows cost £5300' come from?

Of course, can see it now!

I would have said that 4 bulls and 8 cows cost £4000,
so a bull and 2 cows must cost £1000.
Add another cow to get a bull and 3 cows and the price goes up to £1300,
so the extra cow must have cost £300
You then know two lots of £300 plus the cost of the bull is £1000.
That's what I like about maths, there's usually more than one way of getting to the answer

Thanks for the replies. I like that way russett - nice and straightforward. Wish I'd thought of it myself!!