Question

The sum of 3 numbers is 61. The second number is 5 times the first. While the 3rd is 2 less then the first. How do you find the numbers?

Answer 1

`9`, `45`, and `7`

Explanation:

Let's say that your numbers are `x`, `y`, and `z`.

The first thing to write down is that their sum is equal to `61`

`x + y + z = 61" " " "color(purple)((1))`

Next, you know that the second number, `y`, is five times bigger than the first, `x`. This is equivalent to saying that you need to multiply `x` by `5` to get `y`

`y = 5 * x" " " "color(purple)((2))`

Finally, you know that if you subtract `2` from `x` you get the `z`

`z = x - 2" " " "color(purple)((3))`

Use equations `color(purple)((2))` and `color(purple)((3))` to find the value of `x` in equation `color(purple)((1))`

`x + 5x + x - 2 =61`

`7x = 63 implies x = 63/7 = color(green)(9)`

Now take this value of `x` and find `y` and `z`

`y = 5 * (9) = color(green)(45)`

`z = (9) - 2 = color(green)(7)`

The three numbers are `9`, `45`, and `7`.