there-are-40-people-teachers-students-and-workers-in-a-school-and-there-are-40-apples-on-the-table-one-teacher-can-eat-4-apples-and-one-student-can-eat-2-apples-4-workers-can-eat-one-apple

Question Number 180648 by lazyboy last updated on 15/Nov/22

t h e r e a r e 40 p e o p l e

(t e a c h e r s s t u d e n t s a n d w o r k e r s)

i n a s c h o o l . a n d t h e r e a r e 40 a p p l e s

o n t h e t a b l e . o n e t e a c h e r c a n e a t

4 a p p l e s . a n d o n e s t u d e n t c a n e a t

2 a p p l e s . 4 w o r k e r s c a n e a t o n e

a p p l e . f i n d t h e n u m b e r s o f t e a c h e r

s t u d e n t s a n d w o r k e r s

w h o e a t a p p l e s .

p l e a s e h e l p m e .

Commented by Acem last updated on 14/Nov/22

T o a v o i d s o l v i n g b y e x p e r i m e n t, {i t}^{'} s b e t t e r t o

f i n d e q u a t i o n s

4 a + 2 b + \frac{c}{4} = 40 \dots (1)

a + b + c = 40 \dots (2)

? \dots (3)

Commented by Acem last updated on 15/Nov/22

E i t h e r {t h e r e}^{'} s a w a y t o s o l v e s u c h t h i s p r o b l e m

o t h e r w i s e i t {s h o u d n}^{'} t a s k s u c h q u e s t i o n s \dots

Commented by Acem last updated on 15/Nov/22

A t d i s t r i b u t i o n o f t h e e s t a t e, w e c a l c u l a t e

t h e s h a r e s a n d i t r a t i o, b u t w e n e v e r c o u n t h o w

m a n y s o n s, d a u g h t e r s, s i s t e r s, w i f e \dots e t c h e h a d

Commented by Acem last updated on 15/Nov/22

A n y w a y i h a t e d t h i s q u e s t i o n s o m u c h

b e c a u s e i t g i v e s t o t h e c h i l d r e n a n i m p r e s s i o n

t h a t t h e w o r k e r s a r e l e s s v a l u e t h a n t h e o t h e r s

Commented by a.lgnaoui last updated on 15/Nov/22

32 a + 24 b + 17 c = 400 (3)

Commented by Frix last updated on 15/Nov/22

Acem, there i s a way to solve this problem .

Not everything is solveable with formulas,

i . e . Diophantine Equations .

Another example, I once played the game

Tetris . You got points for each filled line,

depending on how many lines you filled at

once :

1 line = 1 point

2 lines = 3 points

3 lines = 6 points

4 lines = 10 points

If you made 100 points, which possible

combinations of lines did you fill when

you filled 31 lines ?

Answered by Acem last updated on 15/Nov/22

@ L a z y B o y, a s l o n g a s {y o u}^{'} r e l a z y, s o r e l a x a n d

g o t o y o u r s c h o o l w i t h o u t s o l v i n g i t, t e l l i n g y o u r

t e a c h e r t h a t y o u r e f u s e t h e i n j u s t i c e a g a i n s t

t h e w o r k e r s . I t h i n k t h a t y o u r s c h o o l a d m i n i s t r a t i o n

w o u l d g i v e y o u a b a d g e o f h o n o r .

Answered by mr W last updated on 15/Nov/22

x t e a c h e r s

y s t u d e n t s

z w o r k e r s w i t h z = 4 k

x + y + 4 k = 40

\Rightarrow x = 40 - y - 4 k

4 x + 2 y + k = 40

4 (40 - y - 4 k) + 2 y + k = 40

2 y + 15 k = 120

\Rightarrow y = 15 n + 45 ⩾ 0 \Rightarrow n ⩾ - 3

\Rightarrow k = - 2 n + 2

\Rightarrow x = - 7 n - 13 ⩾ 0 \Rightarrow n ⩽ - 2

\Rightarrow z = 4 (- 2 n + 2) = 8 - 8 n ⩾ 0 \Rightarrow n ⩽ 1

g e n e r a l s o l u t i o n i s

x = - 7 n - 13

y = 15 n + 45

z = 8 - 8 n

w i t h n = - 3 o r - 2

i . e . (x, y, z) = (8, 0, 32) o r (1, 15, 24)

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