The sum of two numbers is 38. The greater number is 5 more twice the lesser number. What is the greater of the two numbers?

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Answer 1

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Answer 2

I would set this up as:

 

let: lesser number = x

      greater number = 2x + 5

 

Restating the word problem:

lesser number + greater number = 38

         x           +  2x + 5             = 38

 

Solving:  3x + 5 = 38

                   - 5     -5

              ---------------

               3x      =  33

               ---          ---

                3            3

                x        =  11

 

Substitution for the greater number:

         2(11) + 5

           22    + 5

               27

 

Go Get Your "A"!

Answer 3

Hi

 

first, you want to translate these sentences to math:

"the sum of two numbers,(let's call them A and B), is 38"

 

"The sum", means     +

 

"of two numbers" are the things added. (we named them A and B)

 

"is"  means   =

 

SO, A+B=38

 

NEXT

 

"the greater number is 5 more twice the lesser number".

 

We are still talking about the numbers we named A and B above. We know one is larger than the other, so A>B, or B>A. I am choosing A>B because it seems easier to remember.

 

SO we called the "greater number" A,

 

"is" means =

 

"5 more"  means +5

 

"twice the lesser number", means 2 * B, because we chose A to be the greater number.

 

Putting that altogether, we have :

 

A=5 +(2*B)

 

Heres the first part again:

 

A+B=38

A>B

and

A=5+(2B)

 

We know the "greater number" is A

What is the greater of the two numbers?

is the last part of the question.

so lets solve for A

 

this is where you need to substitute 

 

We need A= to start both equations.

 

We have A+B=38 and

             A=5+2B

 

  A+B=38

    -B  -B

   ______

A= 38-B

 

now we can say A=38-B and

                       A=5+2B

 

it stands to reason that   A=38-B =5+2B,

SO

 

 

38-B=5+2B

    +B    +B

__________

38=  5+3B

-5     -5

_________

33 =3B

 

now that we have gotten all the addition and subtraction done, we have 1 variable(or letter B in this case. we are still solving for A..allmost done!)

to get B by itself, we must multiply by the RECIPROCAL of the CoEFFICIENT

 

What number is with our VARIABLE? 

 

         3B

the 3 is the coefficient,

the B is the variable (A is a variable too)

the reciprocal of  3  is    1\3

33\3=3B\3

11=B

we know A=5+2B

so A=5+(2*11)

A=5+22

A=27

 Good luck!  :)