Respuesta :
Using a system of equations, it is found that:
- She has 34 tulips.
- She has 38 daffodils.
- She has 102 hyacinths.
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This question is solved using a system of equations, considering that:
- x is the number of tulips.
- y is the number of daffodils.
- z is the number hyacinths.
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- Half as many tulips as daffodils, thus: [tex]x = \frac{y}{2}[/tex], or [tex]y = 2x[/tex]
- Three times as many hyacinths as tulips, thus [tex]z = 3x[/tex]
- Total of 204, thus [tex]x + y + z = 204[/tex]
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- We have y and z as functions of x, thus we can replace into the third equation and find the amount of tulips.
[tex]x + y + z = 204[/tex]
[tex]x + 2x + 3x = 204[/tex]
[tex]6x = 204[/tex]
[tex]x = \frac{204}{6}[/tex]
[tex]x = 34[/tex]
She has 34 tulips.
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- With the number of tulips, we can find the number of daffodils and hyacinths.
[tex]y = 2x = 2(34) = 38[/tex]
[tex]z = 3x = 3(34) = 102[/tex]
She has 38 daffodils.
She has 102 hyacinths.
A similar problem is given at https://brainly.com/question/17096268
