help with geometry

[cursive anchor]

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[sterile nova]

also a question @wet rover had:

[wet rover]

yes

can u pls help me with that

pls

[sterile nova]

i havent really checked this approach so idk if youll get under 1000
place all 12 boys in rows and then just consider how many girls you need to place in each row then

to get 10 a column

hm

like you need to space the boys out in that row

solve a smaller problem first perhaps

start with 3 boys in each row and 2 girls

[wet rover]

k

rc = 12r+10c+1

[sterile nova]

and empty chair

[wet rover]

right?

[sterile nova]

yea

[wet rover]

thats why +1

[sterile nova]

hmm systems bash lol

wait hold up you can just find interger solutions for that lmao

oh yea

[wet rover]

?

[sterile nova]

do you know simons favourite factoring trick

[wet rover]

no

whats that

?

[sterile nova]

okay so you want to factor your expression into

(r-a)(c-b)=d

where a,b,d are constants

and r and c are your unknowns

then r-a and c-b are factors of d

actually where did you get this question

is there a specific way they want you to solve it/

[wet rover]

no

but i just figured out rc=12r+10c+1

[sterile nova]

okay so move all the varaibles to one side

rc-12r-10c=1

now factor r(c-12)-10c=1

now you need to make -10c factor into something(c-12) by adding a constant value

[wet rover]

we cant factor this

[sterile nova]

ill give you an example

ab-4a-2b=1

a(b-4)-2b=1

add 8 to both sides

a(b-4)-2b+8=9

now factor -2 from -2b+8 to get -2(b-4)

a(b-4)-2(b-4)=9

and factor out b-4

(b-4)(a-2)=9

and if we want integer a and b

b-4 and a-2 are factors of 9

so 1,9 3,3 9,1

:D

[wet rover]

oh k

do i have to use simons factorisation?

[sterile nova]

well there probably is another solution

but thats what i came up with

[wet rover]

wait lemme first learn the simons

[wet rover]

I'm struck what do I do next?

@sterile nova

[sterile nova]

what are the factors of 121?

[wet rover]

1,11,121

Is that correct

@sterile nova

[sterile nova]

well the empty chair is still a chair

[wet rover]

oh ye

so would it be 483?

@sterile nova

just r*c

[sterile nova]

yea

[wet rover]

so is the answer 483 chairs

@sterile nova

[sterile nova]

yes

[wet rover]

tysm

can u do me another favour pls

@sterile nova

[sterile nova]

uhhh no i need to make dinner apologies

might come back later

[wet rover]

k