Question

aflati numerele m,p,q stiind ca sunt invers proportionale cu numerele 2;3;6 si ca m+q-p=8
5;6;10si ca 3m+2p+q=$62 supra 75$
va rog ajutatima dau coroana

Answer 1

[ m;  p;  q ]   i. p.  [  2;  3;  6]  

⇒ 2 m = 3 p = 6 q = k

⇒  m = k / 2;   p = k / 3;  q = k / 6

m + p - q = 8

k / 2 + k / 3 - k / 6 = 8

3 k + 2 k -  k = 6 × 8

4 k = 48

k = 48 : 4  ⇒  k = 12

m = 12 / 2  ⇒  m = 6

p = 12 / 3  ⇒   p = 4

q = 12 / 6  ⇒   q = 2

____________________

a doua cerinta:

[ m;  p;  q ]  i.p.  [  5;  6;  10 ]  

⇒ 5 m = 6 p = 10 p = k

⇒  m = k / 5;   p = k / 6    si   p = k / 10

3 m + 2 p + q = 62 / 75

3 × k / 5  +  2 × k / 6 + k / 10 = 62 / 75

18 k / 30 + 10 k / 30 + 3 k / 30 = 62 / 75

31 k / 30 = 62 / 75

75 × 31 k = 30 × 62

k = ( 30 × 62 ) : ( 75 × 31 )

k = 4 / 5

m = k / 5 = 4 / 5 : 5 = 4 / 5 × 1 / 5  ⇒ m  = 4 / 25

p = k / 6  ⇒  p = 4 / 30  

q= k / 10 ⇒  q  = 4 / 50