4-2^2+5x3-2=11

[Bill]

A could be (4-2)^2=4 surely?

I'm betting the 3 and 2 in the second half have been transposed.

[chemistry]

For background, my son is 13 so this is (supposed to be) a ‘year 9’ level problem.

I strongly suspect a typo, but we’ll see...

[annodomini2]

4x4Tyke said:

chemistry said:

Here’s the original question; note there’s a bag of sweets resting on this...

What age group/key stage is this supposed to be ?

I think we can also conclude we are looking for a value of 1 from 1(1) or (1)(1) because (11) doesn't change the value, so there is no point to adding brackets to the RHS.

Given the way the power is written as a superscript, I think that can conclude that is 'as is' unchanged by brackets.

Given A = "4 - 2²"
The largest value for A is zero, as is, the smallest is -16.

Given B = "5 * 3 - 2"
Then B will always be positive, the smallest value is 5, from "5 * (3 - 2)" larger than A.

There for A + B = 1 or 11

So it is actually impossible if the RHS = 1 since we would need a way to get a negative number from B, but we can't.

The clue doesn't actually help, I'm certain there is a transcription or maths error from the teacher.

Edited by 4x4Tyke on Saturday 13th October 00:16

You can get -30 from B as you state it

[TR4man]

I'll bet that I'm not the only one who doesn't even understand the question, let alone can attempt to answer it!

...and your son is only 13? Crikey I wasn't doing anything like this when I was 13 (or any age for that matter).

[4x4Tyke]

Bill said:

A could be (4-2)^2=4 surely?

We've been assuming that.

Since it is written in the problem as a superscript, "4 - 2²" rather than "4 - 2^2" I was trying to explore that as a subset of solutions, essentially looking to prove that "2²" without brackets could never provide a solution, that it was a null hypothesis for the subset of solutions with "2²" used as is.

Edited by 4x4Tyke on Saturday 13th October 10:13

[4x4Tyke]

annodomini2 said:

You can get -30 from B as you state it

How have you made that negative?

I can't see that.

[V8LM]

Can't be done.

The sum (11) is odd. Therefore, the sum has to be of an odd and an even number.

There are two ways to get an odd number in the left hand side, by using the 3 to multiply an odd number, or using the 5 to multiply an odd number.

The three can appear as either on its own in a bracket as (3-2).

If the three appears on its own, then so does the 2.

If the 3 were to multiply the 5 to get 15, we must add brackets to 4-2^2 to get -2. This can't be done: 4-2^2 = 0; (4-2)^2 = 4; 4(-2)^2 = 16; 4(-(2^2)) = -16; (4(-2))^2 = 64.

If the 3 were to multiply the 5 in brackets, then we must add brackets to 4-2^2+5 to get 13/3. We can't get fractions using sums of integers and integer powers.

So the 3 must appear in a bracket with the 2 to get (3-2).

Therefore, we must add brackets to 4-2^2+5 to get 11. The 5 has to appear on its own to get the odd sum as all the other integers are even.

So we must add brackets to 4-2^2 to get 6. This can't be done.

Edited by V8LM on Saturday 13th October 13:34

[4x4Tyke]

So the correct answer is that this is impossible.

So we need to prove that, to earn chemistry's son the chocolate buttons.

I've going to have a go at a brute force proof with Java.

[chemistry]

Blimey guys, don’t go overboard! I only posted here because I was SO frustrated not being able to do it and so wanted to check I wasn’t missing something!

For what it’s worth, my son has submitted an answer (11, but stating he’s assuming a typo i.e. -5 not + 5) to show he’d tried (he had, for ages!)!

As soon as I have the official ‘answer’, I’ll post it here.

[V8LM]

4x4Tyke said:

So we need to prove that, to earn chemistry's son the chocolate buttons.

I think the post above may be proof. 😊

[chemistry]

Maybe it’s a lesson in Man Maths i.e. the correct answer is:

11 (So yes, you can afford that sports car).

[Mr Pointy]

This sort of problem often turns out to involve trickery on the part of the setter. If this is the case, & the correct answer does not involve simple placement of brackets, then I suggest you complain to the school board to have the teacher disciplined.

It would be a trick, for instance, to reveal that the RHS is written as (1)(1) as it's relying on an inconsistent interpretation of the multiplier notation (5x3 on the LHS, 11 on the RHS). These sort of questions serve only to inflate the setters ego & do nothing to teach those trying to answer the question. There have been enough numerate posters failing to find an answer on this thread to indicate that deception is almost certainly involved.

[V8LM]

Still doesn’t work with (1)(1).

How about (x = 13/15) ?

[JuanCarlosFandango]

Mr Pointy said:

This sort of problem often turns out to involve trickery on the part of the setter. If this is the case, & the correct answer does not involve simple placement of brackets, then I suggest you complain to the school board to have the teacher disciplined.

It would be a trick, for instance, to reveal that the RHS is written as (1)(1) as it's relying on an inconsistent interpretation of the multiplier notation (5x3 on the LHS, 11 on the RHS). These sort of questions serve only to inflate the setters ego & do nothing to teach those trying to answer the question. There have been enough numerate posters failing to find an answer on this thread to indicate that deception is almost certainly involved.

Don't necessarily agree. It's woken up seized and rusty parts of my brain by challenging lazy assumptions and making me think laterally.

On that theme, if you put the brackets in big black marker over the 4 and the superscript 2 you get:

(-2)+(5*3)-2=11

Solved.

[4x4Tyke]

chemistry said:

Blimey guys, don’t go overboard! I only posted here because I was SO frustrated not being able to do it and so wanted to check I wasn’t missing something!

For what it’s worth, my son has submitted an answer (11, but stating he’s assuming a typo i.e. -5 not + 5) to show he’d tried (he had, for ages!)!

As soon as I have the official ‘answer’, I’ll post it here.

It's piqued my interest.

V8LM said:

4x4Tyke said:

So we need to prove that, to earn chemistry's son the chocolate buttons.

I think the post above may be proof. ??

Yes, I cannot see any problems with your proof, that's why I said I thought the correct answer is that it is impossible.

I trying to prove it by an alternate means because...

[Wiccan of Darkness]

chemistry said:

For background, my son is 13 so this is (supposed to be) a ‘year 9’ level problem.

I strongly suspect a typo, but we’ll see...

Aha!! Year 9. He'll have covered expanding brackets in algebra, but the question only asks to add brackets, doesn't say anything about not doing expansions and adding further brackets.

I also note the reward offers a treat of 'your choice'.

Pics of the teacher please....

Meanwhile, considering the fact he's year 9 and would have done expanding brackets, I would hazard a guess that my solution earlier is in fact correct. I did try with the notion that brackets could be on the right of the equation too, but that confused me even more and I erupted in itchy welts and hives.

[annodomini2]

4x4Tyke said:

annodomini2 said:

You can get -30 from B as you state it

How have you made that negative?

I can't see that.

(5 * 3)(-2)

[jet_noise]

annodomini2 said:

4x4Tyke said:

annodomini2 said:

You can get -30 from B as you state it

How have you made that negative?

I can't see that.

(5 * 3)(-2)

Implied operator again. Is that in or outside the "rules"?

[dodgyviper]

hab1966 said:

If it is -11 as an answer then as already noted by others, 4(-2^2) + 5*(3-2) = -11

Surely that's 21 not -11?

Damn those brackets

4(-(2^2)) = -16

In actual fact, my phone calculator worked it out from the first equation, however I agree it doesn't look right - second one looks better

[dodgyviper]

Thinking outside the cubey shaped thing

It's not a multiplication sign, it's an x (algebra)

(4-2^2)+5x(3-2)=11
(0) +5x(1)=11
5x=11
x=11/5
x= 2.2