"Ten increased by [...] is -15" means we add something to 10 and the result is -15.
"The quotient of a number and 2" means a number divided by 2.
That means the we are looking for a number we divide by 2 and the result of that division added to 10 make it -15.
So the number we need to add to 10 to make it -15 would be -25.
The number we need to divide by 2 to get that -25 would be -50.