Question

Vă rog urgent dau coroana​

Answer 1

Fie m, x, y  sumele avute de, respectiv, de mama, Ana și Bogdan.

$\it m>x\ cu\ 15\ \Rightarrow\ m=x+15\ \Rightarrow\ x=m-15\ \ \ \ \ (1)\\ \\ m>y\ cu\ 12\ \Rightarrow\ m=y+12\ \Rightarrow\ y=m-12\ \ \ \ \ \ (2)$

$\it m-a-b=x+a=y+b\ \stackrel{(1),(2)}{\Longrightarrow}\ m- a-b=m-15+a=m-12+b\\ \\ m-15+a=m-12+b|_{-m} \ \Rightarrow\ a-15=b-12}\ \Rightarrow\ a-b=15-12\ \Rightarrow\ \\ \\ \ \Rightarrow\ a-b=3\ \ \ \ \ \ (3)\\ \\ m-a-b=m-15+a|_{-m}\ \Rightarrow\ -a-b=a-15\ \Rightarrow\ -b=a-15+a\ \Rightarrow\ \\ \\ \ \Rightarrow\ -b=2a-15|_{\cdot(-1)}\ \Rightarrow\ b=15-2a\ \ \ \ \ \ (4)\\ \\ (3),\ (4)\ \Rightarrow\ a-15+2a=3\ \Rightarrow\ a+2a=3+15\ \Rightarrow\ 3a=18|_{:3}\ \Rightarrow\ a=6$

$\it a=6\ \stackrel{(4)}{\Longrightarrow}\ b=15-12=3\\ \\ a\cdot b=6\cdot3=18$