A 42-inch board was cut into two pieces. Four times the length of the second piece is equal to the sum of the length of the other piece and thirteen.

Question

Set up equation but do not solve please 

Answer 1

Hi Mariella.

 

A picture would be helpful...  

 

Assume the dashed line below is the board

 

|--------------------------------------|

 

 <----------    42  ----------------->

 

 

If we cut it into two pieces, one piece we will call x,

the other piece will be (42 - x) -- that is the whole board

(42) - the part we cut off (x) will tell us the size

of the remaining piece.   

 

So now our board looks like this:

 

|----------|---------------------------|

      x                     42 - x

 

For ease of math calculations, we will let

the first piece be the (42-x) part of the board, 

and we will let the second piece be the (x) part

of the board.

 

So translating those words into our problem:

 

4  times the length of the 2nd piece     means    

 

4 * (length of 2nd piece) = 4 * x   or "4x"

 

is equal to      means  "="

 

the sum of the other piece (42-x) and 13      means     "42-x+13"

 

So putting all of this together, we have

 

4x = 42 - x + 13

 

 

And that is the set up equation.

Answer 2

y=1st piece

X=2nd piece

4x=y+13

42=y+(y+13)/4

 

Answer 3

Let L1 = the length of the first piece

Let L2 = the length of the second piece

 

We are told the total length of the board is 42 inches, so we can make the following equation:

L1 + L2 = 42

 

We are also told that 4 times the length of the second piece (4*L2) equals the sum of the length of the other piece and 13 (L1 + 13). So we can make the following equation:

 

4*L2 = L1 + 13

 

You now have two equations and two unknowns so you can solve by substitution.