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) $210(t-5)=41,790$

View step-by-step help

Home

Math Problems

Algebra 2

Solve a system of equations in three variables using elimination

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

Identify Problem: The problem involves finding the correct equation that represents the situation described. MacDonald had an initial number of trees, $t$ . After removing $5$ trees, the remaining trees produced $210$ oranges each, for a total of $41,790$ oranges. We need to find the equation that correctly models this situation.
Understand Situation: First, let's understand the situation. MacDonald starts with $t$ trees. After removing $5$ trees, he is left with $t-5$ trees. Each of these remaining trees produces $210$ oranges. The total production from these trees is $41,790$ oranges. The equation to represent this situation should involve multiplying the number of remaining trees $(t-5)$ by the number of oranges each tree produces $(210)$ to get the total number of oranges $(41,790)$ .
Eliminate Incorrect Options: Looking at the options, we can eliminate (A) and (C) because they do not correctly represent the situation described. Option (A) has the total number of oranges multiplied by $t-5$ , which doesn't make sense in this context. Option (C) incorrectly subtracts $-5$ from $210t$ , which does not match the situation of removing $-5$ trees before calculating the total orange production.
Correct Equation Representation: Option (B) suggests adding $5$ to $t$ before multiplying by $210$ , which does not match the situation where $5$ trees are removed from the initial count. Therefore, option (B) is also incorrect.
Correct Equation Representation: Option (B) suggests adding $5$ to $t$ before multiplying by $210$ , which does not match the situation where $5$ trees are removed from the initial count. Therefore, option (B) is also incorrect.Option (D) correctly represents the situation: $210(t-5)=41,790$ . This equation states that the total number of oranges ( $41,790$ ) is equal to the production per tree ( $210$ ) multiplied by the number of trees after removing $5$ ( $t-5$ ). This matches the description of the problem accurately.