Question

One number is 2/3 of another number. The sum of the two numbers is 10. How do you find the two numbers?

Answer 1

The two numbers are `4` and `6`.

Explanation:

Let one number be represented as `x` and the other as `y`.

According to the problem:

`x=2/3y` and `x+y=10`

From the second equation we get:

`x+y=10`

`:.color(red)(y=10-x)` (subtracting `x` from both sides)

Replacing the value of `y` in the first equation we get:

`x=2/3color(red)(y)`

`x=2/3color(red)((10-x))`

Multiplying both sides by `3` we get:

`3x=2(10-x)`

Opening the brackets and simplifying we get:

`3x=20-2x`

Add `2x` to both sides.

`5x=20`

Divide both sides by `5`.

`x=4`

Since from the second equation we have:

`x+y=10`

substituting `x` with `4` we get:

`4+y=10`

Subtract `4` from both sides.

`y=6`

Answer 2

The numbers are 4 and 6.

Explanation:

This question can also be done by using just one variable.
Define each variable and then form an equation.

Let the larger number be `x`.
The other number is `2/3x`

The sum of the numbers is 10.

`x+2/3x = 10" "larr` multiply by 3

`3x + (3xx2x)/3 = 30`

`3x + 2x = 30`

`5x = 30`

`x = 30/5= 6" "larr`this is the larger number

`2/3 (6) = 4" "larr` this is the smaller number.

The numbers are 4 and 6.