Question 1068208
first question:


Building A is 338 meters taller than building B. If the height of building A is subtracted from twice the height of building​ B, the result is 131 meters. How tall is each​ skyscraper? 


let a = the height of building A and b = the height of building B.


you get a = b + 338


if you subtract the height of building A from twice the height of building B, then you get:


2b - a = 131.


you have 2 equations to be solved simultaneously.


they are:


a = b + 338
2b - a = 131


in the second equation, replace a with its equivalent value from the first equation to get:


2b - (b + 338) = 131


simplify to get 2b - b - 338 = 131


combine like terms to get b - 338 = 131


add 338 to both sides of the equaiton to get b = 469.


that's the height of building B.


since building A is 338 meters higher than that, then building A must be 807 meters high.


you get building A is 807 meters high and building B is 469 meters high.


building A is 807 - 469 = 338 meters higher than building B.


if you subtract the height of building A from twice the height of building B, you get 2 * 469 - 807 = 938 - 807 = 131 meters difference.


solution to the first question looks good.


building A is 807 meters high and building B is 469 meters high.


second question:


During his tennis career in singles​ play, John won 33 fewer tournament A titles than tournament B titles and 22 more tournament C titles than tournament B titles. If he won 20 of these titles​ total, how many times did he win each​ one?


let a = number of tournament A titles won.
let b = number of tournament B titles won.
let c = number of tournament C titles won.


since total number tournament titles won is 20, you get:


a + b + c = 20


since he won 33 fewer tournament A titles than tourament B titles, you get:


a = b - 33


since he won 22 more tournament C titles than tournament B titles, you get:


c = b + 22.


replacing a and c with their equivalent values from the first 2 equations, you get the third equation becoming:


b - 33 + b + b + 22 = 20


combine like terms to get 3b - 11 = 20


add 11 to both sides to get 3b = 31


divide both sides by 3 to get b = 10 and 1/3.


since a = b - 33, this makes a = - (22 and 2/3).


since c = b + 22, this makes c = 32 and 1/3.


a + b + c = 20, but .....


a is negative which can't be, indicating there is something wrong with the equation.


i suspect that the total number of tournaments won have to be a number greater than or equal to 33 in order for a to be greater than or equal to 0.


i don't believe there is a valid solution to this problem the way it is presented.


first of all, the value of b was not an integer.


second of all, the value of a is negative.


these are two indications that there is something wrong with the equation the way it is presented.


i suspect the problem is in the number of tournaments won, but that's just a guess.