Came across this puzzle for an 8 year old

[Natasha1]

TL;DR Summary: This should be a simple maths problem

Can anyone solve this as I can't. I found it in my son's school book which we cannot do. (see picture attached).

 

[Ibix]

If you're allowed to assume that two of a symbol is twice the value of one of it (so the first line is three candles plus two hats) then yes, it's a system of simultaneous equations. If not, no, it's not possible.

Even with that assumption that's quite a challenge for an eight year old. My son is fifteen and has just finished studying simultaneous equations, and I gather that three-variable equations like this one is an A-level (17-18 year old) topic. This page covers solving two variable equations and this one covers three variable equations like you have here.

 

[marcusl]

Mentor note: Post edited as it originally provided too much help.
Agreed that it is not an appropriate problem for an 8 year old. Here's how to solve it using elimination/substitution.
Call hats H, candles C and mugs M. Solve the three equations for these variables.
Now you can find their product in #4.

 

[PeroK]

If in doubt, trial and error. The first equation implies the candle is an even number.

 

[Ibix]

I'd say the simplest approach is to look at the second and third equations. The difference on the right hand sides is 2, the difference on the left hand sides should tell you something about hat and candle. With that, you should be able to get hat or candle from the first equation. At that point it should all unravel.

I agree that writing them as H, C abd M will make the algebra easier.

 

[phyzguy]

I bet there are some 8 year olds that could solve it. There is nothing wrong with a challenging problem that makes you think.

 

[mcastillo356]

Hi @Natasha1

It's linear algebra. Call $x$ to the doll, or candle (I don't know what represents), $y$ to the cap, and $z$ to the cup. It goes like this:

$$\begin{align*}
x+2y+2x&=52\\
z+2z+2x&=41\\
2z+z+2y&=43\\
\end{align*}$$

Greetings

 

[Math100]

Is this really a math problem for eight-year old students? How come I have doubts?

 

[Mark44]

Is this really a math problem for eight-year old students? How come I have doubts?

Yeah, me too.

 

[berkeman]

Is this really a math problem for eight-year old students? How come I have doubts?

Well, it turns out the OP has a history here at PF of posting undergraduate math problems (often with no effort shown). So you might be able to read between the lines...

 

[gmax137]

It looks to me like the kind of thing that pops up in Facebook or Instagram, posted by someone trying to get a lot of comments. At least this one has a definite answer, unlike the 6 + 2 x 4 ÷ 3 nonsense.

 

[bob012345]

TL;DR Summary: This should be a simple maths problem

Can anyone solve this as I can't. I found it in my son's school book which we cannot do. (see picture attached).

View attachment 355339

Please give the book reference so we can see it in context. Thanks.

 

[rcgldr]

Reminds me of the guy that was so proud he solved a puzzle in 2 hours when the box stated 3 to 5 years.