The cost of 6 pens and 3 pencils is 84. One third of the cost of one pen is equal to the cost of one pencil. What is the total cost of 4 pens and 5 pencils.
Answers
cost of pencil=X/3
6X +3 (X/3) = 84
6x+X=84
7X=84
X=12
4 pens =4X = 48
-5 pencils=5 (X/3)=20
total cost=68
hope it helps
Concept:
Replace the unknown two quantities by variables and make suitable mathematical equations and solving the equations we get the specified.
Given:
Given that one third cost of pen is cost of pencil and total cost of 6 pens and three pencils is 84.
Find:
The total cost of 4 pens and 5 pencils.
Solution:
Let the value of 1 pen be x and price one pencil be y.
According to given information, cost of 6 pens and three pencils is 84.
So,
6x + 3y = 84
3(2x+y) = 84
2x+y = 84/3
2x+y = 28........................(i)
Also it's providing one third of cost of 1 pen is that the cost of 1 pencil.
x/3 = y
x = 3y ..................(ii)
Substituting (ii) in (i) we get,
2*3y+y = 28
6y+y = 28
7y = 28
y = 28/7
y = 4
Putting y=4 within the equation (ii) we get,
x = 3*4 = 12
So the cost 4 pens and 5 pencils = 4x+5y = 4*12 + 5*4 = 48 + 20 = 68
Hence the overall cost of 4 pens and 5 pencils is 68.
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