Question 968847: One number is bigger than another number. When one third of smaller number is taken away from a half of the bigger number the answer is 10. What is the smaller number?
How do you do it ?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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