The gardeners should buy 48 white and 116 pink hydrangeas altogether
Step-by-step explanation:
The given is:
- The gardeners at Middleton Place Gardens want to plant a total of 45 white and pink hydrangeas in one flower bed
- In another flower bed, they want to plant 119 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
We need to find how many white and how many pink hydrangeas the gardeners should buy altogether
Assume that the number of white hydrangeas is x and the number of pink hydrangeas in the first bed
∵ The first bed has x white hydrangeas
∵ The first bed has y pink hydrangeas
∵ The total of white and pink hydrangeas in 1st bed is 45
- Equate the sum of x and y by 45
∴ x + y = 45 ⇒ (1)
∵ In the 2nd bed the number of the white hydrangeas is 2 times
as in the 1st bed
∵ The number of the pink hydrangeas is 3 times as in the 1st bed
∵ The number of the hydrangeas in the 2nd bed is 119
- Multiply x by 2 and y by 3, then add the products and equate
the sum by 119
∴ 2x + 3y = 119 ⇒ (2)
Now let us solve the system of equations
Multiply equation (1) by -3 to eliminate y
∵ -3x - 3y = -135 ⇒ (3)
- Add equations (2) and (3)
∴ -x = -16
- Divide both sides by -1
∴ x = 16
- Substitute the value of x in equation (1) to find y
∵ 16 + y = 45
- Subtract 16 from both sides
∴ y = 29
∵ The number of the white hydrangeas in the 1st bed is x
∵ The number of the white hydrangeas in the 2nd bed is 2x
∴ The total number of the white hydrangeas = x + 2x = 3x
∵ x = 16
∴ The total number of the white hydrangeas = 3(16) = 48
∵ The number of the pink hydrangeas in the 1st bed is y
∵ The number of the pink hydrangeas in the 2nd bed is 3y
∴ The total number of the pink hydrangeas = y + 3y = 4y
∵ y = 29
∴ The total number of the pink hydrangeas = 4(29) = 116
The gardeners should buy 48 white and 116 pink hydrangeas altogether
Learn more:
You can learn more about the system of equations in brainly.com/question/6075514
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