SOLUTION: A boy bought two note books and two pens for Ghc 6.50. His sister bought one note book and two pens for Ghc 3.50. What was the cost of a note book and the cost of the pen.?

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Question 1151616: A boy bought two note books and two pens for Ghc 6.50. His sister bought one note book and two pens for Ghc 3.50. What was the cost of a note book and the cost of the pen.?
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
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let the cost of a note book be n and the cost of the pen p
A boy bought two note books and two pens for Ghc 6.50.
2n%2B2p=6.50......both sides divide by 2
n%2Bp=6.50%2F2
n%2Bp=3.25......solve for n
n=3.25-p.............eq.1

His sister bought one note book and two pens for Ghc 3.50.
n%2B2p=3.50.....solve for n
n=3.50-2p...........eq.2
from eq.1 and eq.2 we have
3.25-p=3.50-2p.....solve for p
2p-p=3.50-3.25
p=0.25
go back to
n=3.25-p.............eq.1, substitute p
n=3.25-0.25
n=3.00

the cost of a note book is 3.00 and the cost of the pen is 0.25


Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.

            This problem is SPECIALLY INTENDED to solve it mentally in 2 minutes.

            This mental solution is as follows. 


2 notebooks and 2 pens cost 6.50

1 notebook and 2 pens cost 3.50.


It is totally clear from it (even for 3-rd grade student) that 1 notebook costs the difference 6.50-3.50 = 3 Ghc.


Then two pens cost 3.50 - 3 = 0.50 Ghc.


ANSWER.  One notebook costs 3 Ghc.  One pen costs 0.25 Ghc.

---------------

The lesson to learn from my solution is THIS : 

    Always read the condition attentively.

    It may happen that you can solve the problem mentally in two lines, instead of using and solving equations.


Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
A boy bought two note books and two pens for Ghc 6.50. His sister bought one note book and two pens for Ghc 3.50. What was the cost of a note book and the cost of the pen.?
Let cost of a pen be p, and a notebook, n

Then we get: 2n + 2p = 6.5_____2(n + p) = 2(3.25)____n + p = 3.25 ----- eq (i)

Also, n + 2p = 3.5 ------ eq (ii)

 ---- Subtracting eq (i) from eq (ii)

n + .25 = 3.25 ----- Substituting .25 for p in eq (i)