Question

A garden shop charges $72 for 3 rose bushes and 2 lilac bushes. It also charges $114 for 5 rose bushes and 3 lilac bushes. At these same rates, how much would the garden shop charge for 1 rose bush and 1 lilac bush?

Answer 1

They would charge $28.80 for 1 rose bush and 1 lilac bush. $72/5 flower bushes = $14.40. Thats the price of one bush. Since you're getting 2 bushes, multiply that by 2, and get 28.80.

Answer 2

Amount charges for 1 rose bush =
`\$12`

Amount charges for 1 lilac bush =
`\$18`

Explanation:

Let x denotes cost of one rose bush and y denotes cost of one lilac bush.

Given statement 1: A garden shop charges $72 for 3 rose bushes and 2 lilac bushes.

we get ,

3x+2y = 72 ....(i)

Given statemnet 2: A garden shop charges $114 for 5 rose bushes and 3 lilac bushes.

we get ,

5x+3y=114 ...(ii)

From equation1,
`x=(72-2y)/(3)`

On this value of x in equation (ii), we get

`5\left ( (72-2y)/(3) \right )+3y=114\\360-10y+9y=342\\y=360-342\\=18\\\Rightarrow x=(72-2y)/(3)\\=(72-2(18))/(3)\\=(72-36)/(3)\\=(36)/(3)\\\\=12`

So,

Amount charges for 1 rose bush =
`\$12`

Amount charges for 1 lilac bush =
`\$18`