Allen is 5 years older than Cassandra. In 4 years, he will be twice as old as Cassandra was 2 years ago. Find their ages

Answer 1

Hello! I'm teacher Shelley. I'll try to work this through for you.

Let's use A for Allen and C for Cassandra. We'll need to use two equations to solve this problem.

Allen is 5 years older than Cassandra.

A=C+5

In 4 years, he will be twice as old as Cassandra was 2 years ago.

A+4= (C-2)2

Let's work the right side first.

2C-4

A+4=2C-4

A+4+4=2C

A+8=2C

Now let's pull in the first equation.

A=C+5 (Put C+5 in for A)

C+5 +8=2C (Add numbers)

C+13=2C

13=C (subtract left C from both sides)

Now we know Cassandra's age is 13. Let's plug that into the original equation.

A=C+5 (or A=13+5)

A=18

So Allen is 18 and Cassandra is 13

Plug that back into the second equation to check it.

A+4= (C-2)2

18+4=(13-2)2

22=11(2)

22=22

Hope that helps!