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15 A man bought
x hectares of land for
$R. He used
y hectares to build a house for himself and sold the remainder at
$z a hectare more than what he paid for it. He found that he received
$R for the land he sold. Express
R in terms of
x,y and
z.

$15$ A man bought $x$ hectares of land for $\$ R$ . He used $y$ hectares to build a house for himself and sold the remainder at $\$ z$ a hectare more than what he paid for it. He found that he received $\$ R$ for the land he sold. Express $R$ in terms of $x, y$ and $z$ .

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Write and solve direct variation equations

Full solution

Q.

15

A man bought

x

hectares of land for

\$ R

. He used

y

hectares to build a house for himself and sold the remainder at

\$ z

a hectare more than what he paid for it. He found that he received

\$ R

for the land he sold. Express

R

in terms of

x, y

and

z

.

Calculate Price per Hectare: The man bought $x$ hectares for $\$R$ , so the price per hectare is $\frac{R}{x}$ .
Calculate Hectares Sold: He sold $(x - y)$ hectares, because he used $y$ hectares for his house.
Calculate Selling Price per Hectare: He sold each of the remaining hectares for $(R/x + z)$ dollars.
Calculate Total Amount Received: The total amount he received for the land he sold is x - y) * (R/x + z)\.
Set Equation for Total Amount: He received \(\$R for the land he sold, so we set the equation: $R = (x - y) \times (\frac{R}{x} + z)$ .
Solve for Total Amount: Now, we solve for $R$ : $R = (x - y) \times (R/x) + (x - y) \times z$ .
Solve for Total Amount: Now, we solve for $R$ : $R = (x - y) \times (R/x) + (x - y) \times z$ .This simplifies to: $R = R - (y \times R/x) + (x - y) \times z$ .

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