Question

The sum of two numbers is 30. the sum of the greater number and three times the lesser number is 54. how do you find the numbers?

don't understand how find numbers

Answer 1

a and b `a+b=30` and follow explanation.......Your numbers are 12 and 18.

Explanation:

a is the small number and b is the greater (than a) number:

`a+b=30`

`b+3a = 54`

Arrange these (multiply the second by `-1`):

`a+b=30`

`-3a - b = -54`

Sum these, yielding
`-2a = -54+30`

`-2a = -24`
`a=12`

Since `a+b=30`, you can find b now:

`12+b = 30`

`b=30-12 = 18`

`b=18`

Answer 2

Let us assume the two numbers to be `color(red)(x and y`.

According to the question, we have,

`color(green)(=>x+y=30` `color(white)("xxxxxxxxxxxxxx"` `color(green)(......."Eq 1"`

`=>x=30-y`

`color(green)(=>x+3y=54` `color(white)("xxxxxxnxxxxxx"` `color(green)(......."Eq 2"`

Replacing `(x=30-y)`

`=>(30-y)+3y=54`

`=>30+2y=54`

`=>2y=54-30`

`=>2y=24`

`=>y=24/2`

`color(blue)(=>y=12`

Now let us find `x`

`"Eq 1"=x+y=30`

`=>x+12=30`

`=>x=30-12`

`color(blue)(=>x=18`

`therefore` The two numbers are `color(darkorange)(12 and 18`

~Hope this helps! :)