One number is five more than two times another. If their sum is increased by four, the result is twenty-seven. Find the numbers.

Question

what are the numbers

 

Answer 1

This is a system of two algebraic equations

Lets call the "One number" "y"

and the other one "x"

 

So this would make the first equation:

y=5+2x (One number is five more than two times another)

 

Next you have to make the second equation using the second sentence:

x+y (their sum) +4 (is increased by 4) = 27 (the result is 27)

x+y+4=27

 

After some quick algebra you have two equations:

y=5+2x

y=23-x

 

Next use substitution to find one of the variables. Lets replace "y" in the first equation with what "y=" in the second equation:

23-x=5+2x

 

solve for x:

23-x=5+2x

-5+x  -5 +x

18=3x

divide by 3 on both sides to isolate x:

6=x

 

Now that you know what x is you can plug that x into either equation to find the corresponding y:

y=5+2(6)

y=5+12

y=17

 

The final answer is the first number (y) is 17 and the second number (x) is 6