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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?
Choose 1 answer:
(A)
41,790(t-5)=200
(B)
210(t+5)=41,790
(c)
210 t-5=41,790
(D)
210(t-5)=41,790

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? $\newline$ Choose $1$ answer: $\newline$ (A) $41,790(t-5)=200$ $\newline$ (B) $210(t+5)=41,790$ $\newline$ (C) $210 t-5=41,790$ $\newline$ (D) $210(t-5)=41,790$

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Write a linear inequality: word problems

Full solution

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?

\newline

Choose

1

answer:

\newline

(A)

41,790(t-5)=200

\newline

(B)

210(t+5)=41,790

\newline

(C)

210 t-5=41,790

\newline

(D)

210(t-5)=41,790

Initial Trees Count: Let's denote the initial number of trees on MacDonald's farm as $t$ . After removing $5$ trees, the number of remaining trees is $(t - 5)$ . Each of these remaining trees produced $210$ oranges. The total number of oranges produced by these trees is given as $41,790$ .
Equation Derivation: To find the equation that represents the situation, we multiply the number of remaining trees by the number of oranges each tree produced to get the total harvest. This gives us the equation: $210 \times (t - 5) = 41,790$ .
Option Evaluation: Now, let's check each option to see which one matches our derived equation: $\newline$ (A) $41,790(t-5)=200$ is incorrect because it suggests that the total number of oranges is a function of the initial number of trees, which doesn't make sense in this context.
Correct Equation: $(B) 210(t+5)=41,790$ is incorrect because it adds $5$ trees instead of subtracting them, which does not match the situation where $5$ trees were removed.
Correct Equation: $(B) 210(t+5)=41,790$ is incorrect because it adds $5$ trees instead of subtracting them, which does not match the situation where $5$ trees were removed.(C) $210t-5=41,790$ is incorrect because it subtracts $5$ oranges instead of accounting for the removal of $5$ trees.
Correct Equation: (B) $210(t+5)=41,790$ is incorrect because it adds $5$ trees instead of subtracting them, which does not match the situation where $5$ trees were removed.(C) $210t-5=41,790$ is incorrect because it subtracts $5$ oranges instead of accounting for the removal of $5$ trees.(D) $210(t-5)=41,790$ is correct because it matches our derived equation, representing the total harvest from the remaining trees after $5$ trees were removed.

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