What is the answer to this?

Question

Find two numbers such that one number is 1/2 more than 1/4 the other number and the sum of the numbers is 9 . What is the value of the smaller number?

Answer 1

This is an exercise in translating (ambiguous) English into (unambiguous) math.

And as such it is partially an art, prone to error and misinterpretation.

But here is how I would translate it:

English: "Find two numbers such that"

Math: "Find x, y"

English: "one number"

Math: "x"

English: "is"

Math: "="

English: "1/2 more than"

Math: "x/2 +"

English: "1/4 the other number"

Math: "y/4"

English: "and"

Math: Start a new constraint relating to the same numbers x, y

English: "the sum of the numbers"

Math: "x+y"

English: "is"

Math: "="

English: "9"

Math: "9"

So we have two constraints:

x = x/2 + y/4

x + y = 9

Solving these two equations:

x = 3, y = 6

Answer 2

Let the numbers be represented by x and y.

x + y = 9 (sum of the numbers is 9)

y= 1/4 (x) + 1/2 (one number (y) IS 1/2 more than 1/4 of the other number (x))

Let's use substitution to solve this system.

x + [1/4 (x) + 1/2] = 9 (replace y in 1st equation with its equivalent in terms of x from 2nd equation).

Multiply through by 4 to remove fractions (multiplication property for equality):

4x + x + 2 = 36

5x = 34

x = 34/5

So 34/5 + y = 9

y = 45/5 - 34/5 = 11/5

So solution is:

x = 34/5

y = 11/5

Check:

34/5 + 11/5 = 45/5 = 9.

11/5 =? 1/4 (34/5) + 1/2

11/5 =? 17/10 + 5/10

11/5 =? 22/10

11/5 = 11/5 (check)

Answer 3

x+y/8=9

8x+y=72

There's more than 1 answer.

Or are you saying 8+x+y=9?