word problem, Find the cost of the pen

Question

Bert bought a notebook, a pen,and yellow paper for his son. The total cost was P32.00.
The notebook costsP4.00 less than a pen. The pen cost P12.00 more than a paper. Find the cost of the pen.

Answer 1

If X= the notebook, Y= the pen, and Z= the paper, this can be represented by the following system of equations:

 

X+Y+Z=32

X=Y-4

Z=Y-12

 

Substituting the equivalent values with Y into the original equation, you get:

 

(Y-4) + Y + (Y-12) = 32

    3Y - 16 = 32

        3Y = 48

          Y = 16

The cost of the pen is 16

Answer 2

Let N=price of notebook, P=price of pen, Y=price of yellow paper.  

 

N+P+Y=32 (the total cost is 32)

P-N=4        (the pen is 4 more expensive that the notebook

P-Y=12       (the pen costs 12 more that the yellow paper)

 

Now isolate N and Y in the last two equations.

P-4=N

P-12=Y

Plug these formulas for N and Y into the first equation.

(P-4) + P + (P-12) = 32

Now use algebra to isolate the variable P

3P -16 = 32

3p = 32+16=48

Finally, P = (48/3) = 16 bucks  

TaDa!