Question

James uses 1/3 of his land for growing durains, 1/4 for bananas,3/8 for Guavas and the remaining 9 hectares for mangoes. What is the total area of his land?

Answer 1

Greetings and Happy Holidays!

Let x represent the total area of land

We can create an equation to solve for the unknown, this being the total area:

`x= (1)/(3)x+ (1)/(4)x+ (3)/(8)x+9`

Combine like terms (terms with the same variable and degree):

`x= (1)/(3)x+ (2)/(8)x+ (3)/(8)x+9`


`x= (1)/(3)x+(5)/(8)x+9`


`x= (8)/(24)x+(15)/(24)x+9`


`x=(23)/(24)x+9`

Add
`-(23)/(24)x` to both sides.

`(x)+(-(23)/(24)x)=((23)/(24)x+9)+(-(23)/(24)x)`


`x-(23)/(24)x=9`


`(24)/(24)x-(23)/(24)x=9`


`(1)/(24)x=9`

Divide both sides by
`(1)/(24)`

`((1)/(24)x)/((1)/(24))=(9)/((1)/(24))`


`x=(9)((24)/(1))`


`x=((9)/(1))((24)/(1))`


`x=(216)/(1)`


`x=216`

The Answer Is:

`\left[\begin{array}{ccc}x=216\end{array}\right]`

James has 216 square units of land.

Hope this helps!
-Benjamin