Question

patriția are cu 3 ani mai mult decăt fratele său george si de 4 ori mai putin decat mama.Tata este cu 4 ani mai mare decat mama afla ce varsta are fiecare stiind ca in total au 111 ani.​

Answer 1

Răspuns:

g = p - 3

m = 4p

t = 4p + 4

p + g + m + t = 111

inlocuim

p + p - 3 + 4p + 4p + 4 = 111

10p = 111 + 3 - 4

10p = 110

p = 11 (ani) Patricia

g = 11 - 3 = 8 (ani) George

m = 4p = 44 (ani) mama

t = 44 + 4 = 48 (ani) tata

Answer 2

$\it p>g\ cu\ 3\ \Rightarrow p=g+3\ \ \ \ \ (1)\\ \\ p<m\ de\ 4\ ori\ \Rightarrow m>p\ de\ 4\ ori \Rightarrow m=4p \stackrel{(1)}{\Longrightarrow} m=4g+12\ \ \ \ \ \ (2)\\ \\ t>m\ cu\ 4 \Rightarrow t=m+4 \stackrel{(2)}{\Longrightarrow} t=4g+16\ \ \ \ (3)$

$\it p+g+m+t=111 \stackrel{(1),(2),(3)}{\Longrightarrow}\ g+3+g+4g+12+4g+16=111 \Rightarrow\\ \\ \Rightarrow 10g+31=111|_{-31} \Rightarrow 10g=80 \Rightarrow g=8\ ani\ \ \ \ \ (4)\\ \\ (1),\ (4) \Rightarrow p=8+3=11\ ani\\ \\ (2),\ (4) \Rightarrow m=4\cdot8+12=44\ ani\\ \\ (3),\ (4) \Rightarrow t=4\cdot8+16=48\ ani$