Question

The sum of two numbers is 180 and the larger number exceeds four times the smaller number by ten, what are the 2 numbers?

Answer 1

The numbers are `110` and `70`.

Explanation:

Be `x` and `y` the two numbers. We know that

`x+y=180` and that

`x=y+4*10`

If we replace `x` with `y+40` we find

`y+40+y=2y+40=180`

`rarr 2y=180-40=140`
`rarr y=140/2=70`

Then we find

`x=70+40=110`

`rarr x+y=110+70=180`

Answer 2

The numbers are: `34` and `146`

Explanation:

The problem is to find such numbers, that:

1. Their sum is 180
2. Larger number exceeds 4 times the smaller by 10.

These conditions lead to folowing system of equations:

`{(x+y=180),(y=4x+10):}`

If we substitute `y` in yje first equation we get:

`x+4x+10=180`
`5x+10=180`
`5x=170`
`x=34`

Now we can substitute `x` in any equation to calculate `y`:

`y=4*34+10`
`y=136+10`
`y=146`

Finally we can write the answer:

`{(x=34),(y=136):}`