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 $n$. Given that it costs GH¢950.00 to produce 600 bricks and GH¢1030.00 to produce 1000 bricks, we need to find the relationship between $c$, $h$, and $n$, and then calculate the cost of producing 500 bricks.

1. Problem Description

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 $n$. Given that it costs GH¢950.00 to produce 600 bricks and GH¢1030.00 to produce 1000 bricks, we need to find the relationship between $c$, $h$, and $n$, and then calculate the cost of producing 500 bricks.

2. Solution Steps

The problem states that $c = h + y$, where $y$ varies directly as $n$. This means $y = kn$ for some constant $k$. Therefore, we can write the cost as:

$c = h + kn$

We are given two data points:

1. When $n = 600$, $c = 950$.

2. When $n = 1000$, $c = 1030$.

We can use these points to set up a system of two equations with two unknowns, $h$ and $k$:

$950 = h + 600k$ (1)

$1030 = h + 1000k$ (2)

Subtracting equation (1) from equation (2):

$1030 - 950 = (h + 1000k) - (h + 600k)$

$80 = 400k$

$k = \frac{80}{400} = \frac{1}{5} = 0.2$

Now, substitute $k = 0.2$ into equation (1):

$950 = h + 600(0.2)$

$950 = h + 120$

$h = 950 - 120 = 830$

Therefore, the relationship between $c$, $h$, and $n$ is:

$c = 830 + 0.2n$

Now, we need to find the cost of producing 500 bricks, i.e., when $n = 500$.

$c = 830 + 0.2(500)$

$c = 830 + 100$

$c = 930$

3. Final Answer

(i) The relationship between $c$, $h$, and $n$ is $c = 830 + 0.2n$.

(ii) The cost of producing 500 bricks is GH¢930.

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