Question

In an orchard there are 360 trees and they are distributed in 9 rows with the same number of trees in each row. 2 are rows of orange trees, 4 of apple trees and the rest are of pear trees. What fraction of the trees in the orchard are of each type of fruit tree? How many trees of each type are there?

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Answer to a math question In an orchard there are 360 trees and they are distributed in 9 rows with the same number of trees in each row. 2 are rows of orange trees, 4 of apple trees and the rest are of pear trees. What fraction of the trees in the orchard are of each type of fruit tree? How many trees of each type are there?

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Tiffany
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65 Answers
Para encontrar la fracción de árboles de cada tipo de frutal, primero necesitamos saber cuántas filas hay en total.

Dado que hay 360 árboles y cada fila tiene el mismo número de árboles, podemos encontrar el número de filas dividiendo el total de árboles entre el número de árboles en cada fila.

\text{Número de filas} = \frac{360}{\text{Árboles por fila}}

Como hay 9 filas y cada una tiene el mismo número de árboles, podemos determinar el número de árboles en cada fila dividiendo el total de árboles entre el número de filas.

\text{Árboles por fila} = \frac{360}{\text{Número de filas}}

Ahora que sabemos el número de filas y el número de árboles por fila, podemos determinar la fracción de árboles de cada tipo de frutal.

Las 2 filas de naranjos representan \frac{2}{\text{Número de filas}} de los árboles totales.

Las 4 filas de manzanos representan \frac{4}{\text{Número de filas}} de los árboles totales.

Y el resto de filas (que son de perales) representan \frac{\text{Número de filas} - 2 - 4}{\text{Número de filas}} de los árboles totales.

Ahora podemos calcular el número de árboles de cada tipo multiplicando la fracción por el total de árboles.

Árboles de naranjos: \frac{2}{\text{Número de filas}} \times 360

Árboles de manzanos: \frac{4}{\text{Número de filas}} \times 360

Árboles de perales: \left( \frac{\text{Número de filas} - 2 - 4}{\text{Número de filas}} \right) \times 360

Finalmente, podemos simplificar las fracciones, calcular el número de filas y sustituir los valores para encontrar el número de árboles de cada tipo y su fracción correspondiente.

Respuesta:

Número de filas: \text{Número de filas} = \frac{360}{\text{Árboles por fila}} = \frac{360}{\frac{360}{9}} = 9

Árboles por fila: \text{Árboles por fila} = \frac{360}{\text{Número de filas}} = \frac{360}{9} = 40

Árboles de naranjos: \frac{2}{\text{Número de filas}} \times 360 = \frac{2}{9} \times 360 = 80

Árboles de manzanos: \frac{4}{\text{Número de filas}} \times 360 = \frac{4}{9} \times 360 = 160

Árboles de perales: \left( \frac{\text{Número de filas} - 2 - 4}{\text{Número de filas}} \right) \times 360 = \left( \frac{9 - 2 - 4}{9} \right) \times 360 = \frac{3}{9} \times 360 =120

Por lo tanto, la fracción de los árboles del huerto que son de cada tipo de frutal es:

Naranjos: \frac{80}{360} = \frac{2}{9}

Manzanos: \frac{160}{360} = \frac{4}{9}

Peras: \frac{120}{360} = \frac{3}{9} = \frac{1}{3}

En el huerto hay:

80 árboles de naranjos

160 árboles de manzanos

120 árboles de perales

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