How do I do a problem that says one number is five less then twice another . If the product of the two numbers is 117 find the numbers

Question

One number is five less than twice another if the product of two numbers is 117 find the numbers

Answer 1

Hi Ashley,  I always tell my students "number for number, letter for letter, symbol for symbol...you write what it says"

There are two variables talked about in the problem...so there will normally be two equations.

 

Some things to keep in mind...vocabulary

 

 

Less than means subtract and switch

When it asks for a number...you write a letter (variable)

product of means that you will multiply the two things that come after the words "Product of"

 

_______________________________________________________________________________

 

One number      is     five    less than      twice    another number

 

    x                 =     5          - switch        2times    y

 

 

So, now that I have written everything right under the words...I will switch it for the less than

 

  x =   2y - 5

__________________________________________________________________________

 

Product of the two numbers is 117

                      

                       x y             =  117

 

 

__________________________________________________________________________

 

Now you can solve this two ways from here...

 

1)  if you know how to factor a quadratic function, substitute and solve.

 

2)  If you do not know how to factor a quadratic, consider what two numbers divide into 117.

     117 = 13 x 9

     117 = 3 x 39

 

     so if you were to try to plug in 13 and 9 into both of the equations, would it make sense?  If so, you have found your answers.  Otherwise try to plug in 3 and 39.

 

 

 

 

                

 

 

 

 

Answer 2

Let x = one number, y= other number

x=2y-5

xy=117

(2y-5)y=117

2y²-5y-117=0

(2y+13)(y-9)=0

Either 2y+13=0 and y=-13/2, x=-18  or

y=9, x=13

There is no restriction on the sign the numbers, and so either set of solutions is correct.