one number is 4 less than 3 times another. Their sum is negative16. find the smaller number.

Question

I'm having some trouble finding the equation for this problem and then solving it. can someone please take me through the steps. Thank you.

Answer 1

Hi Mike,

 

Sometimes the hardest part of solving the equation is writing the "number sentence" from the "word sentence"...

 

So first some meanings of words...where the "word sentence" says "a number" you will write "a letter" (also known as a variable).  So when it starts off "one number" you will write a letter, like x.

 

Less than means to subtract and to switch...you have to do both or the answer will not be correct.  Here is why...  Think about what 3 less than 7 is...you know that the answer to this one is 4.  BUT, 3-7 is not 4.  This is where the switch comes in   when we say 3 less than 7...we know in our head that we are subtracting 7-3...so less than mean subtract and switch.

 

Sum means to add.

 

So lets put it all together...(I like to write my number sentence above my word sentence so that I don't forget anything)

 

 

                  x         =        4      -(switch)      3y              x   +  y  =  -16

one number is 4 less than 3 times another. Their sum is negative16. find the smaller number.

 

now I do the switching around

 

            x    =     3y    -    4                          x   +   y  =  -16

 

Hope this helps

 

 

Answer 2

Let x and y be the two numbers.

 

 

y = 3x - 4

 

x + y = -16

 

 

Substitute the first equation into the second:

 

x + (3x - 4) = -16

 

4x - 4 = -16

 

4x = -12

 

x = -3

 

So, y = 3(-3) - 4 = -9 - 4 = -13

 

 

The smaller number is -13.