WAEC Mathematics Question 2015 ( Essay Question Six 6b )

QUESTION 6b

(b) The cost (c) of producing n bricks is the sum of a fixed amount, h, and a variable amount, y, where y varies directly as n. If it costs GH¢950.00 to produce 600 bricks and GH¢ 1,030.00 to produce 1000 bricks,

(i) Find the relationship between c, h and n ; 

(ii) Calculate the cost of producing 500 bricks.

SOLUTION

From the statement, we have

where K is constant

Substituting y = Kn into the equation we have;

c = h + Kn ........................(i)

Where c = 950 , n = 600

 950 = h + 600K ....................(a)

Also, where c =  1030, n = 1000

We have 1030 = h + 1000K .................(b)

Solving equation (a) and equation (b) simutaniously

950 = h + 600K ...................(a)

1030=h + 1000K..................(b)

Subtracting equation (a) from equation (b)

(1030-950) = (h-h) + (1000K-600K)

80= 400K

Substituting  into equation (a) , we have;

When 5 goes into 600 we will have 120,

So, therefore

950 = h + 120

h = 950-120

h = 830

Hence;

(i) To obtain the relationship between c, h and  n, we have 

c = h + Kn

   Answer

(ii) The cost of producing 500 bricks

ie. n = 500

Given

(500 divided by 55 gives us 100)

So therefore,

c = 830 + 100 

c = GH¢ 930 ANSWER

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