Question

three consecutive numbers. The sum of the first and second is 20 more than third.what is number

Answer 1

Answer:

There are three consecutive numbers. The sum of the first two is 20 more than the third. What are the numbers?

r,s, t={21, 22, and 23}

PREMISES

r+s+t=a series of three (3) consecutive numbers

r+s=t+20

ASSUMPTIONS

Let r, s, and t=three consecutive numbers

Let r=the value of r

Let s=the value of r+1 in terms of r [f(s)=r+1]

Let t=the value of r+2 in terms of r [f(t)=r+2]

CALCULATIONS

r+s=t+20

r+(r+1)=(r+2)+20

2r+1=r+22

2r-r+(1–1)=(r-r)+(22–1)

r+0=0+21

r=21

and,

if s and t=r+1 and r+2 respectively, then

r, s, and t=

{21, 22, and 23}

PROOF

If r, s, and t={21, 22, and 23}, then the equations

r+s=t+20

21+22=23+20 and

43=43 establish three roots (zeros) r, s, and t={21, 22, and 23} of the mathematical statement r+s=t+20

Answer 2

Answer:

r+s+t=a series of three (3) consecutive numbers

r+s=t+20

 Let r, s, and t=three consecutive numbers

Let r=the value of r

Let s=the value of r+1 in terms of r [f(s)=r+1]

Let t=the value of r+2 in terms of r [f(t)=r+2]

 r+s=t+20

r+(r+1)=(r+2)+20

2r+1=r+22

2r-r+(1–1)=(r-r)+(22–1)

r+0=0+21

r=21

and,

if s and t=r+1 and r+2 respectively, then

r, s, and t=

{21, 22, and 23}

PROOF

If r, s, and t={21, 22, and 23}, then the equations

r+s=t+20

21+22=23+20 and

43=43 establish three roots (zeros) r, s, and t={21, 22, and 23} of the mathematical statement r+s=t+20