story problem

Question

Two numbers sum to be -27. Three times the first number and four times the second number sum to be -160. Find the two numbers.  

 

Set up as a story problem with variables and 2 equations. 

Answer 1

Always need to assign variables (letters) to each thing that can change.

 

So lets let the first number be "x" and the second number be "y".

 

x+y=-27  that comes from the first sentence.  

 

3x + 4y = -160  that comes from the second sentence.

 

 

If you multiply the top equation by -3, you can eliminate the x variable.

 

-3x + -3y  = +81

  3x +  4y = -160

 

Now add vertically and get that y=-79.

 

Now just use that in x+y=-27 to find x.

 

x+(-79)=-27

 

Add 79 to both sides

 

x=52

 

Now check:

 

Do x+y=-27?  52+(-79)=-27  YES!

 

Does 3(52)+4(-79) = -160?    YES!  so we have found the solution

 

x=52  (the first number)

y=-79 (the second number)