Question

Determina numerele naturale mnpr si s așezale in ordine descrescătoare știind ca acestea îndeplinesc simultan condițiile: m+n=12 m+p=14, m+r=16,m+s=18,si
n+p+r+s=42

Answer 1

m+n=12=>n=12-m
m+p=14=>p=14-m
m+r=16=>r=16-m
m+s=18=>s=18-m
n+p+r+s=42
  Inlocuim:
(12-m)+(14-m)+(16-m)+(18-m)=42
12-m+14-m+16-m+18-m=42
12+14+16+18-m-m-m-m=42
60-4m=42
4m=60-42
4m=18
m=18/4
m=9/2
Inlocuim pe "m" in urmatoarele:
n=12-m=>n=12-9/2=>n=15/2
p=14-m=>14-9/2=>p=19/2
r=16-m=>r=16-9/2=>r=23/2
s=18-m=>s=18-9/2=>s=27/2
n+p+r+s=42
15/2+19/2+23/2+27/2=42
Verificare:
(15+19+23+27)/2=84/2=42

(m+n)+(m+p)+(m+r)+(m+s)=12+14+16+18
m+m+m+m+n+p+r+s=12+14+16+18
n+p+r+s=42
m+m+m+m+42=12+14+16+18
4m+42=12+14+16+18
4m+42=60
4m=60-42
4m=18
m=18/4=>m=9/2
si apoi inlocuiesti....e bine?
n=12-m=>n=12-9/2=>n=15/2
p=14-m=>14-9/2=>p=19/2
r=16-m=>r=16-9/2=>r=23/2
s=18-m=>s=18-9/2=>s=27/2