Question

12.) Pete has two older siblings. His older brother, Tom, is twice his age. His older sister, Sarah, is four years older than Pete. The sum of their three ages is 44. What are the ages of all three siblings? *

Answer 1

We should understand that we need to model the real situation with some equations and the we will solve them: first we need to define carefully our variables

- P: the age of Peter

-T: the age of Tom

- S: the age of sara

then we need to put the information that is given to us in a mathematical form:

-when they said to us that His older brother, Tom, is twice his age. that means:

`T=2P`

-And when they say to us that His older sister, Sarah, is four years older than Peter. that means:

`S=P+4`

-then they said to us that the sum of their three ages is 44, so:

`S+P+T=44`

lets solve these three equations:

lets subtitute the first two equations in the last one:

`S+P+T=(P+4)+P+(2P)=44`

the we wil solve this to find P

`(P+P+2P)+4=4P+4=4(P+1)=44`

then

`4(P+1)=44\Rightarrow P+1=(44)/(4)\Rightarrow P+1=11\Rightarrow P=11-1=10`

then the age of peter is P=10, then substituing this result in the first two equations the age of Tom is T=2(10)=20 and the age of Sara is S=10+4=14