Answer:
Cost of one bush = x = $9
Cost of one bonsai tree = y = $32
Step-by-step explanation:
Let Cost of one bush = x
Cost of one bonsai tree = y
From the expression: A company paid $ 391 for 15 bushes and 8 bonsai trees
We made equation: ![15x+8y=391](https://tex.z-dn.net/?f=15x%2B8y%3D391)
and From the expression: They had to purchase 9 more bushes and 5 more bonsai trees for $ 241 , we made equation: ![9x+5y=241](https://tex.z-dn.net/?f=9x%2B5y%3D241)
Solving both equations simultaneously we can find value of x and y
Let:
![15x+8y=391--eq(1)\\9x+5y=241--eq(2)](https://tex.z-dn.net/?f=15x%2B8y%3D391--eq%281%29%5C%5C9x%2B5y%3D241--eq%282%29)
We will use elimination method to solve these equations.
Multiply eq(1) by 5 and eq(2) by 8 and subtract
![75x+49y=1955\\72x+40y=1928\\- \ \ \ - \ \ \ \ \ \ \ -\\--------\\3x=27\\x=\frac{27}{3}\\x=9](https://tex.z-dn.net/?f=75x%2B49y%3D1955%5C%5C72x%2B40y%3D1928%5C%5C-%20%5C%20%5C%20%5C%20-%20%5C%20%5C%20%5C%20%5C%20%20%5C%20%5C%20%5C%20-%5C%5C--------%5C%5C3x%3D27%5C%5Cx%3D%5Cfrac%7B27%7D%7B3%7D%5C%5Cx%3D9)
So, value of x=9
Now finding value of y by putting value of x in equation 1
![15x+8y=391\\Put \ x=9\\15(9)+8y=391\\135+8y=391\\8y=391-135\\8y=256\\y=\frac{256}{8}\\y=32](https://tex.z-dn.net/?f=15x%2B8y%3D391%5C%5CPut%20%5C%20x%3D9%5C%5C15%289%29%2B8y%3D391%5C%5C135%2B8y%3D391%5C%5C8y%3D391-135%5C%5C8y%3D256%5C%5Cy%3D%5Cfrac%7B256%7D%7B8%7D%5C%5Cy%3D32)
So, value of y=32
Cost of one bush = x = $9
Cost of one bonsai tree = y = $32