I need your help... This is my 11 year olds math homework, one of the questions anyway... I cannot work it out.

Mrs choy spent exactly £10 on exactly 100 eggs.

Large eggs cost 50p
Medium eggs cost 10p
Small eggs cost 5p

For two of the sizes, she bought the same number of eggs.

How many of each size did she buy

Suppose she buys x number of large and medium, the number of smalls is (100 - 2x)
We know the total has to add up to 1000 (£10 is 1000p, yes?)
So
50x + 10x + 5(100 - 2x) = 1000
> 60x - 10x + 500 = 1000
> 50x = 500
> x = 10

So 10 of large and medium, 80 small.

If she buys x of large and small and (100 - 2x) of medium
50x + 10(100-2x) + 5x = 1000
>35x = 0
> x = 0
Which makes sense since 100 x 10 is 1000, but I'll reject this solution since we have no large and small eggs.

If she buys x of medium and small and (100 - 2x) of large
50(100 - 2x) + 10x + 5x = 1000
> 5000 -75x = 1000
> x = 4000/75
x is not an integer, so reject this solution.

Hence 10 of large and medium and 80 of small is the correct answer.

Come on that's trivial. You have
1) L*0.5 + M*0.1 * S*0.05 = 10.
2) L + M + S = 100.

Also, L, M and S must be whole numbers greater than or equal to 0.
Plus you have one of these conditions:
L=M or L=S or M=S.

Trying the first condition:

1) L*0.6 + S*0.05 = 10.
<=> 1*) 12*L + S = 200.
2) 2*L + S = 100.

1*) - 2): 10*L = 100. <=> L = 10.
Since L=M, M=10, and S = 100 - 20 = 80.

Checkup:

10 * 0.5 + 10 *0.1 + 80 * 0.05 = 10 Pound.
10 + 10 + 80 = 100 eggs.

Try the second and third condition as homework to see whether they have a solution for whole non-negative numbers L, M, S.

@irene agreed, and I've mentioned that, but if I had to choose one answer between the two I'd go for 10, 10, 80. This is an 11 years old's homework.

God I wish I had that in school right now, not fucking finding a whole function only from knowing these

P(3,0)
P(-2,0)

Possible but aaaa

@irene fair enough
But I wouldn't expect it

@seraphimsystems you might as well give both valid solutions though, you don't lose anything.

@kescherRant if you're given only two points and no other info, isn't it basically just a line?

Or do it the dev way:

@seraphimsystems oops, minor error in case 3, should be 85x not 75x. 4000/85 is still not an integer so it still works.

@irene not quite brute force. Only 18% of the full range. Also, that's what computers are good at, aren't they? ^^

@irene That's Cordia New, and I like it better than the fonts specifically targeted towards devs. Also, lower case Lima and digit one are easy enough to tell apart.

@RememberMe thought of it the same way. Had to look how British currency works though

@irene in the defines at the top. When you zoom in, the difference seems small, but the trick is that the top stroke at One goes diagonally while the one from Lima is horizontal.

The thing with dedicated dev fonts is that they're more clear, but they also are so ugly that I can't bear them.

@RememberMe Nope.
Usually there's additional info like "it's a polynomial function"

@kescherRant still fairly straightforward, that comes down to basically solving linear systems to get the coefficients once you plug in all the values?

I can get how that is irritating though, especially if you make a calculation error somewhere. Been there.

@RememberMe That's why we preferred the "pen and paper only" exams in uni math. Once you got anything else than whole numbers or maybe 0.5, you knew you had an error somewhere.

Besides math, also RPGs are better with pen and paper, but that's another story. ;-)

@Fast-Nop well, unless your teachers set questions with answers like 23.637 (this was a thing in school).

In uni we used calculators for everything upto linear systems with 3 variables (very simple calculators, not those fancy TI ones or whatever). Plenty of paper based symbolic stuff though, I would argue that's harder than manual calculation since calculation is at least straightforward and usually easy to check. The *number* of times I got differential equations wrong because I was in a hurry...

I would like to agree with the RPG statement but I've never played a pen-and-paper RPG so I can't really comment :(

Easy: she bought only medium-sized eggs: 100 eggs à 10p = £10. For two sizes (small and large), she bought the same amount, namely 0.

@kescherRant that one is easy, there's an infinite number of functions that pass trough two points. 😆

Unless you are limited to only linear functions on a 2d plane with no curvature. Then theres just one, but thats boring. 😧

@acz0903 How can I understand you. This school is already in my throat. I'm thinking about taking my daughter to a tutor. When I run into similar problems I open math problem solver, use https://edubirdie.com/math-problem-... to do it. I haven't found any other options yet. But this one suits me 100%. I myself don't know much either.