Let's call the first number m and the second n.
"One number is five more than four times another."
Four times the second number = 4n
Five more than that = 5+4n
Therefore:
m = 5+4n
"If their sum is increased by one the result is 21."
Their sum will be: m + n
Their sum increased by 1 will be: m + n +1
Therefore:
m+n+1 = 21
Now since we know m = 5+4n, we can plug that into the second equation for m:
5+4n+n+1 = 21
We simplify and get:
6+5n = 21
Now we can solve for n:
6+5n-6 = 21-6
5n = 15
5n ÷ 5 = 15÷5
n = 3
Now that we know n=3, we can also solve for m, using m=5+4n
m = 5+4n
m = 5+4(3)
m = 5+12
m = 17
Our answer is that n=3 and m=17.
