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At the beginning of the season, MacDonald had to remove $5$ orange trees from his farm. Each of the remaining trees produced $210$ oranges for a total harvest of $41,790$ oranges. If $t$ is the initial number of trees on MacDonald's farm, which of the following equations best describes the situation?

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Write and solve equations for proportional relationships

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Q. At the beginning of the season, MacDonald had to remove

5

orange trees from his farm. Each of the remaining trees produced

210

oranges for a total harvest of

41,790

oranges. If

t

is the initial number of trees on MacDonald's farm, which of the following equations best describes the situation?

Denote initial number of trees: Let's denote the initial number of trees on MacDonald's farm as $t$ . Since MacDonald had to remove $5$ orange trees, the number of remaining trees is $t - 5$ . Each of these remaining trees produced $210$ oranges. The total harvest from these trees is given as $41,790$ oranges. To find the relationship between the initial number of trees and the total harvest, we can set up the following equation: $\newline$ $(t - 5) \times 210 = 41,790$
Find total harvest equation: Now, we need to solve for $t$ . First, we can simplify the equation by dividing both sides by $210$ to find the number of remaining trees: $(t - 5) = \frac{41,790}{210}$
Solve for number of trees: Perform the division to simplify the equation further: $t - 5 = 199$
Simplify equation further: Next, we add $5$ to both sides of the equation to solve for $t$ : $\newline$ $t = 199 + 5$
Add $5$ to solve: Finally, we perform the addition to find the value of $t$ : $t = 204$

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