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The gardeners at Middleton Place Gardens want to plant a total of 41 white and pink hydrangeas in one flower bed. In another flower bed, they want to plant 108 hydrangeas. In this bed, they want 2 times the number of white hydrangeas and 3 times the number of pink hydrangeas as in the first bed. Use a system of equations to find how many white and how many pink hydrangeas the gardeners should buy altogether.


The gardeners should buy ___ white hydrangeas and ___ pink hydrangeas.

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Answer:

The gardeners should buy 45 white hydrangeas and 104 pink hydrangeas.

Step-by-step explanation:

Let the gardeners at Middleton Place Gardens have to buy x numbers of white hydrangeas and y number of pink hydrangeas.

So, x + y = 41 {Given} ........... (1)

Again, for another flower bed they want to plant 108 hydrangeas, where the number of white ones is 2 times that of Middleton Place Gardens and the number of pink ones is 3 times that of Middleton Place Gardens.

So, 2x + 3y = 108 ........ (2)

Now, solving equations (1) and (2) we get,

3y - 2y = 108 - 82 = 26

⇒ y = 26

And from equation (1) we get,

x = 41 - 26 = 15.

So, the total number of white hydrangeas the gardeners have to buy is (x + 2x) = 3x = 3 × 15 = 45.

And the total number of pink hydrangeas the gardeners have to buy is (y + 3y) = 4y = 4 × 26 = 104. (Answer)

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