Task A-1.7. (10 points)

Ana has four times as many years as Peter had when Ana was as old as Peter is now. When Peter is as old as Ana is now, together they will have 95 years. How old is Ana, and how old is Peter?
## Solution.

Let the number of Ana's years be $A$, and the number of Petar's years be $P$.

Ana had $P$ years (how old Petar is now) $A-P$ years ago.

1 point

$A-P$ years ago, Petar had $P-(A-P)=2P-A$ years, 1 point so according to the problem, Ana is now $4(2P-A)$ years old, hence $A=4(2P-A)$. 1 point

Petar will have $A$ years (how old Ana is now) in $A-P$ years, 1 point and Ana will then have $A+(A-P)=2A-P$ years 1 point so according to the problem, $(2A-P)+A=95$, i.e., $3A-P=95$. 1 point

By solving the obtained system $A=4(2P-A), 3A-P=95$ 1 point

we get $A=40, P=25$.

Ana is 40 years old, and Petar is 25.