Question

Suma a doua numere naturale este de 6 ori mai mare decat diferenta lor,iar diferenta lor este cu 50 mai mica decat suma lor.Sa se afle cele doua numere.

Answer 1

a+ b=6×( a-b)
a+ b=6a-6b
b+6 b=6a-a
7b=5a
b=5a/7
a-b=(a+b)-50
a-5a/7=(a+5a/7)-50
2a/7=12a/7-50
12a/7-2a/7=50
10a/7=50
10a=7×50
a=350:10
a=35
b=(5×35)/7
b=175/7
b=25
Raspuns:a=35
b=25

Answer 2

a + b=6 ×( a - b)

a + b = 6a - 6b⇒b + 6 b = 6a - a⇒7b = 5a

b = 5a/7

a - b = (a + b) - 50

a - 5a/7 = (a + 5a/7)-50

2a/7=12a/7-50

12a/7-2a/7=50⇒10a/7=50⇒10a=7×50⇒a=350:10

a = 35

b=(5×35)/7⇒ b = 175/7

b = 25

a = 35; b = 25