one number is 7 more than twice the other number. if the sum of two numbers is 31, find the two numbers.

Question

need explainations

Answer 1

x=the first number

2x+7=the second number

add them together

x+2x+7=31

3x+7=31

3x=31-7

3x=24

x=24/3

x=8

2x+7=2*8+7=16+7=23

8 and 23 are the numbers

Answer 2

You want to start by assigning variable names and then writing equations for each fact they give you.

 

So let x = the first number and let y be the "other" number.

 

So the first statement means that x = 2y + 7 -- 7 more than twice the other number.

 

And the second statement says that x + y = 31.

 

So that gives you two equations with two unknowns:

 

x = 2y + 7

x + y = 31

 

So you just have to solve these.

 

Since the first equation gives you an easy expression for x, just substitute that into the second equation:

x + y = 31

(2y + 7) + y = 31

3y + 7 = 31

3y = 24

y =  8

 

Since the sum of the two numbers is 31, x must be 23.