The sum of 6 times petra's age and 8 times kathy's age is 162. kathy is 1 year more than twice as old as petra is. find each of their ages.

 Let Petra's age be x Let Kathy's age be y 6x+8y=162 <1 equation y=2x+1 6x + 8(2x+1)=162 6x+16x+8=162 22x=154 x=7 Substituting x in y=2x+1 y=2(7)+1 y=14+1 y=15

Let Petra be "P"
Let Kathy be "K"

Based on given information, we know that 6 times Petras age (6p) plus 8 times Kathy's age (8k) equals 162.
Our first equation is 6p+8k=162

Now for the second half of the problem:
Kathy is one year older (+1) than twice Petra's age (2p)
Our second equation is k=2p+1

Now substitute the first equation back into the first equation using the value of k
6p+8(2p+1)=162
Solve for P
6p+16p+8=162
22p+8-8=162-8
22p/22=154/22
P=7
Now we substitute Petra's age (7) back into the second equation to find Kathy's age.
K=2(7)+1
Solve for k
K=14+1
K=15
To check, put both k and p values into the first equation:
6(7)+8(15)=162
42+120=162
162=162✔️
ANSWER
Petra is 7 years old
Kathy is 15 years old