Eight more than four times a number is the same as two less than five times the number. What is the number?

Question

17348 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-10T15:33:51

The number is 10

First, let's call the number we are looking for $n$ $n$ .

Eight more than four times a number can be written as:

$4 n + 8$ $4n + 8$

Two less than five times the number can be written as:

$5 n - 2$ $5n - 2$

Because these are the same we can write the following equation and solve for $n$ $n$ :

$4 n + 8 = 5 n - 2$ $4n + 8 = 5n - 2$

$4 n - 4 n + 8 + 2 = 5 n - 4 n - 2 + 2$ $4n - 4n + 8 + 2 = 5n - 4n - 2 + 2$

$0 + 8 + 2 = 5 n - 4 n - 0$ $0 + 8 + 2 = 5n - 4n - 0$

$10 = n$ $10 = n$