Question

1. a farmer plants trees in a straight row that is 21 feet long. the trees must be 7 feet from each other. how many trees can be planted in this row? draw a sketch to explain your answer.
2. the segment jl has midpoint m. jm = 3x + 2 and ml = 14 - x. what is the value of x?

a 6
b 3
c 16
d 12

Explanation:

21.

Step1: Calculate number of intervals

The length of the row is 21 feet and the distance between trees is 7 feet. The number of 7 - foot intervals in a 21 - foot row is $\frac{21}{7}=3$.

Step2: Determine number of trees

The number of trees is one more than the number of intervals. So the number of trees $n=3 + 1=4$.

A simple sketch can be made: Draw a straight line representing the 21 - foot row. Mark points on the line such that the distance between consecutive points is 7 feet. You will see that with 3 intervals, there are 4 points (representing trees).

Step1: Use mid - point property

Since M is the mid - point of segment JL, then $JM=ML$. So we set up the equation $3x + 2=14−x$.

Step2: Solve for x

Add x to both sides of the equation: $3x+x + 2=14−x+x$, which simplifies to $4x+2 = 14$.
Subtract 2 from both sides: $4x+2−2=14−2$, getting $4x=12$.
Divide both sides by 4: $\frac{4x}{4}=\frac{12}{4}$, so $x = 3$.

Answer:

4

22.