Ashley spent $228 on 6 rose bushes and 18 shrubs. Heather spent $139 on 8 rose bushes and 9 shrubs. What is the cost of one rose bush and th

Question

Ashley spent $228 on 6 rose bushes and 18 shrubs. Heather spent $139 on 8 rose bushes and 9 shrubs. What is the cost of one rose bush and the cost of one shrub?

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3 months 2022-02-17T15:19:39+00:00 1 Answer 0 views 0

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  1. Emma
    0
    2022-02-17T15:21:29+00:00

    Answer:

    The cost of one rose bush is $5 and the cost of one shrub is $11.

    Step-by-step explanation:

    Given:

    Ashley spent $228 on 6 rose bushes and 18 shrubs.

    Heather spent $139 on 8 rose bushes and 9 shrubs.

    Now, to find the cost of one rose bush and the cost of one shrub.

    Let the cost of one rose bush be [tex]x.[/tex]

    And let the cost of one shrub be [tex]y.[/tex]

    So, the total money Ashley spent on 6 rose bushes and 18 shrubs:

    [tex]6x+18y=228[/tex]

    [tex]6x=228-18y[/tex]

    Dividing both sides by 6 we get:

    [tex]x=38-3y[/tex]   …….(1)

    Now, the total money Heather spent on 8 rose bushes and 9 shrubs are:

    [tex]8x+9y=139[/tex]

    Substituting the value of [tex]x[/tex] from equation (1) we get:

    [tex]8(38-3y)+9y=139[/tex]

    [tex]304-24y+9y=139[/tex]

    [tex]304-15y=139[/tex]

    Subtracting both sides by 304 we get:

    [tex]-15y=-165[/tex]

    Dividing both sides by -15 we get:

    [tex]y=11.[/tex]

    The cost of one shrub = $11.

    Now, substituting the value of [tex]y[/tex] in equation (1) we get:

    [tex]x=38-3y[/tex]

    [tex]x=38-3\times 11[/tex]

    [tex]x=38-33[/tex]

    [tex]x=5.[/tex]

    The cost of one rose bush = $5.

    Therefore, the cost of one rose bush is $5 and the cost of one shrub is $11.

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