SOLUTION: 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

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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