matthew lives 7 km closer to the school than Berthe. They live a total of 31 km from school. how far does each live from the school
Let the distance between matthew and the school be \(x\)
Then, the distance between Berthe and the school is 7 km more than that of matthew; so: \(x+7\) is the distance between Berthe and the school.
"They live a total of 31 km from school"
So, the sum of the distances we wrote above is 31:
\(x+(x+7)=31 \\ \iff 2x+7=31\\ \iff 2x=24\\ x=12\)
So, mathew lives 12 km far, and Berthe lives (12+7)=19 km far.
I hope this helps!