Question 1068208: 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?
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?
John won
nothing tournament A title(s).
John won
nothing tournament B title(s).
John won
nothing tournament C title(s).
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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