Respuesta :
The Solution.
Let the price of a citron be represented with x, and the price of a fragrant wood apple be y.
So, the first sentence in the question gives the equation below:
[tex]5x+3y=27\ldots eqn(1)[/tex]Similarly, the second sentence in the question gives the equation below:
[tex]3x+5y=29\ldots eqn(2)[/tex]Solving the above pair of equations simultaneously using the Elimination Method:
We shall eliminate the term in x;
So, we shall multiply through eqn(1) by 3, we get
[tex]\begin{gathered} 3(5x+3y=27) \\ 15x+9y=81\ldots eqn(3) \end{gathered}[/tex]Similarly, we shall multiply through eqn(2) by 5, we get
[tex]\begin{gathered} 5(3x+5y=29) \\ 15x+25y=145\ldots eqn(4) \end{gathered}[/tex]Subtracting eqn(3) from eqn(4), we have
[tex]\begin{gathered} 15x+25y=145 \\ -(15x+9y=81) \end{gathered}[/tex]We get:
[tex]16y=64[/tex]Dividing both sides by 16, we get
[tex]\begin{gathered} \frac{16y}{16}=\frac{64}{16} \\ \\ y=4 \end{gathered}[/tex]To find x, we shall substitute 4 for y in eqn(1):
[tex]\begin{gathered} 5x+3(4)=27 \\ 5x+12=27 \end{gathered}[/tex]Collecting the like terms, we get
[tex]\begin{gathered} 5x=27-12 \\ 5x=15 \end{gathered}[/tex]Dividing both sides by 5, we get
[tex]\begin{gathered} \frac{5x}{5}=\frac{15}{5} \\ \\ x=3 \end{gathered}[/tex]Therefore, the price of a citron is 3 units, and the price of a fragrant wood apple is 4 units.
