Score of 180cm in highjump gives 627 points and 190cm gives 714 points. 40m discus throw gives 665 points and 45m throw 767 points. James's jump result is 188cm, and discus throw 41m. if the result of the jump deteriorate by 5cm, how much the discus throw result has to get better for the total score to stay the same.
I tried to solve this with no luck, because i have no idea how to even start. It would be great to get some directions on how to solve this.
Adding to what Bram28 and Malcolm said the linear relationships for jumps and throws are
$$jump = 8.7(j-180)+627$$ $$throw = 20.4(t-40)+665$$
This gives James's initial score of 1382. I will leave the rest to you.