Function Machine maths question

[sw059]

Hi can anyone help with this question from CSSE pass paper. Can't figure out the technique to work out the missing information.


Casey is using a different 'multiply then add' number machine. When she inputs 3, the output is 26. When the input is 6, the output is 36.

3 x ? + ? = 26
5 x ? + ? = 36

Fill in the unknown values for Casey's number machine, so you obtain the same input and output values as she did.

Thanks.

[hermanmunster]

Is the second input 5 or 6?

[sw059]

Sorry mistake there the second input is 5 not 6.

Thanks

[2childmum]

I would work out possible answers to the first input, then trial that into the second input

So3x7=21 so you would need to +5 to get to 26. But 5x7+5=40, so that is not correct.

x 6 and+ 8 doesn't work

But x5 and +11 does - 3x5=15 +11=26
and 5x5=25+11=36

[2childmum]

Or you could use algebra - simultaneous equations

3x+y=26
5x+y=36


from the first equation y=26-3x

put that into the second equation 5x+(26-3x)=36

rearrange 5x-3x=36-26
2x=10
x=5

the put that back into the first equation

3(5) +y=26
y=26-15
y=11

[ToadMum]

Or you could use algebra - simultaneous equations

3x+y=26
5x+y=36


from the first equation y=26-3x

put that into the second equation 5x+(26-3x)=36

rearrange 5x-3x=36-26
2x=10
x=5

the put that back into the first equation

3(5) +y=26
y=26-15
y=11

Are simultaneous equations on the year 5 (or year 6) scheme of work in the NC? CSSE doesn't expect any KS3 knowledge (nor should any 11+ exam).

[2childmum]

I wouldn't have thought so -although I don't know. I would imagine that the trial method is what the exam is after. I simply put the algebra version in as it is another way to solve it and I though others may be interested. I'll try not to be so helpful next time.

[ToadMum]

I wouldn't have thought so -although I don't know. I would imagine that the trial method is what the exam is after. I simply put the algebra version in as it is another way to solve it and I though others may be interested. I'll try not to be so helpful next time.

sorry, I appreciate that you may have meant (mainly) how we on here might solve it. However, I did worry slightly that some parents might spend the rest of the holidays making their 10 year olds do algebra after every meal .

(Having now had a rummage in .gov world, I am relieved to discover that simultaneous equations have not found their way into the KS2 curriculum ).

[2childmum]

That's ok and I'm sorry for over-reacting. I was just pleased that I had remembered how to use algebra after so many years. And I'm feeling a bit under the weather struggling with a virus which has bought on asthma. I should have stopped before hitting 'submit'

I'm also glad to hear simultaneous equations haven't made it down to KS2 - I stopped teaching a while ago as I could no longer bring myself to put the children through it all.

Hopefully the trial method makes sense.

[yoyo123]

Simultaneous equations would definitely not be expected at KS2