Question

Afla numerele naturale a, b, c stiind ca sunt invers proportionale cu 2; 4 respectiv 5 si a+2b+c=48

Answer 1

2a = 4b = 5c = k
=>:
a = k / 2
b = k / 4
c = k / 5
a + 2b + c = 48
k/2  + 2k/4 + k/5 = 48
k/2  + k/2 + k/5 = 48
2k/2 + k/5 = 48    Numitorul comun = 10
(10k + 2k) / 10 = 48
12k / 10 = 48
k = 10 * 48 / 12 = 480 / 12 = 40

a = k / 2 = 40 / 2 = 20
b = k / 4 = 40 / 4 = 10
c = k / 5 = 40 / 5 = 8

a = 20
b = 10
c = 8