Family/Age/Linear system/Exercise

${}M,P,S$ and ${}T$ are the members of one family. In this case, ${}M$ is three times as old as ${}S$ and ${}T$ together, ${}M$ is older than ${}P$, and ${}S$ is older than ${}T$, moreover, the age difference between ${}S$ and ${}T$ is twice as large as the difference between ${}M$ and ${}P$. Furthermore, ${}P$ is seven times as old as ${}T$, and the sum of the ages of all family members is equal to the paternal grandmother's age, which is ${}83$.

a) Set up a linear system of equations that expresses the conditions described.

b) Solve this system of equations.

Create a solution