Question 968847
there are an infinite number of values that satisfy this problem statement.


the problem statement is:


one number is bigger than another number.


1/2 * the bigger number minus 1/3 * the smaller number is equal to 10.


let y be the bigger number.


let x be the smaller number.


1/2 * y - 1/3 * x = 10


solve for y to get y = 20 + 2/3 * x.


that's the first equation.


the second equation that has to be satisfied is y > x.


so, what is happening is that y has to be equal to 20 + 2/3 * x and y has to be greater than x at the same time.


these two equations have to be solved simultaneously.


you have:


y = 20 + 2/3 * x
y > x


since y = 20 + 2/3 * x, the second equation can replace y with 20 + 2/3 * x to get:


20 + 2/3 * x > x


subtract 2/3 * x from both sides of this equation to get:


20 > x - 2/3 * x which becomes:


20 > 1/3 * x


multiply both sides of this equation by 3 to get:


60 > x


that's your solution.


x has to be smaller than 60 and y has to be equal to 20 + 2/3 * x.


the problem statement will be satisfied when those two events occur.


for example:


let x = 30.


when x = 30, y has to be equal to 20 + 2/3 * 30 = 20 + 20 = 40.


you have = 30 and y = 40


y is the bigger number.


1/2 * y - 1/3 * x must be equal to 10.


1/2 * 40 - 1/3 * 30 = 20 - 10 = 10


both equations have been satisfied.


your solution is:


y = 20 + 3/2 * x and x < 60.