Question

A company paid $ 391 for 15 bushes and 8 bonsai trees . They had to purchase 9 more bushes and 5 more bonsai trees for $ 241 . What is the cost of each bush and bonsai tree ? the boxes below .

Answer 1

Cost of one bush = x = $9

Cost of one bonsai tree = y = $32

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`

and From the expression: They had to purchase 9 more bushes and 5 more bonsai trees for $ 241 , we made equation:
`9x+5y=241`

Solving both equations simultaneously we can find value of x and y

Let:

`15x+8y=391--eq(1)\\9x+5y=241--eq(2)`

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=(27)/(3)\\x=9`

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=(256)/(8)\\y=32`

So, value of y=32

Cost of one bush = x = $9

Cost of one bonsai tree = y = $32