Help with this 11+ Q please!

[Wallabyone]

I'm hopefully attaching a photo - I need to explain to 9yr old and am struggling 🙈 Thank you!

Using n for limes and m for lemons

6n + 7m = 8n + 4 m therefore
7m - 4m = 8n -6n therefore
3m = 2n therefore
1.5m = 1n therefore
6n x 1.5 +7m = 9m + 7m = 16 m (lemons)

That might be wrong btw I'm not a maths teacher!

That's not a nine year old maths question...

It's for 11+ according to OP so algebra which they do a bit of in year 6. It's only really bodmas and knowing you can't compare apples and pears (or limes and lemons in this case).

6 limes & 7 lemons OR 8 limes and 4 lemons

Without using simultaneous equations formally, logic then tells us that 2 extra limes have been got with the loss of 3 lemons

So every 2 limes is the same as 3 lemons

so 6 limes and 7 lemons is actually 9 lemons and 7 lemons

So 16 lemons in all.

Blah is right in the formal method.

I don't think it is possible to solve. All you can get is that 1 lime = 1.5 lemons. But the equation works with lime costing 3 and lemon 2 as well as lime costing 15 and lemon 10.

I agree-this is not standard maths for year 5 (I'm a primary teacher and I haven't done this stuff since possibly GCSE, the algebra in year 6 is not this level).

Thank you for the last worded explanation-that is what I needed to help explain to him.

Hi, it's simple swapping of algebra to different sides. I for lime and E for lemon...

6I+7E=8I+4E
(7E-4E)=(8I-6I)
3E=2I

So the answer is 16! Hope that helps. I enjoy calculations like this, takes me back to a simpler time... before I had to act like a grown up!

@Jenjenn

I don't think it is possible to solve. All you can get is that 1 lime = 1.5 lemons. But the equation works with lime costing 3 and lemon 2 as well as lime costing 15 and lemon 10.

They haven't asked how much things cost, just how many lemons can be bought. Which can be solved as other answers here have shown.

No grammar school for me today!! I saw the op that day and I’ve only just solved it! So glad I managed to find it on adv. search. Glad I also got 16. But I don’t know how 🤯 !! So I got

So was I right in thinking so i=3 and e=2. Or did I just get lucky?

I mean - can I just read off those figures from their fractions like that?? I don’t think I can… Or is that ok?? I guess any 3/2. It’s still the same figure… like if I got 6/4 that would still get me there. See I calculated price per lemon/lime to work it out. But unnecessary….

A lot more workings! And Easter extravaganza menu thrown in for good measure!

Which 11+ is this? It's not like my daughters one we're preparing for.

(Also she's been advised to skip the odd "long" question that she can't do quickly as its better to finish with lots of marks than stop on a puzzle.)

@Dontfuckingsaycheese Your method is fine. However my more wordy explanation is the way someone who doesn't know algebra should think about it. Method is fundamentally the same.

In maths, any method that gets the correct answer through logic is fine. Which is why I kind of disagree with SATs giving method marks for some methods but not others which I think is what occurs

@TeenPlusCat

Your wordy version helped me get my head round it! I think my diving straight into trying to solve it with equations made me lose sight of what I was actually trying to solve! I still had to check my figures when I’d got them and it felt more like luck than secure logic!! I do love a good maths question!!