Points E, F, and G are plotted on a number line at -1,2,and 6, respectively. Find the coordinate of the point that represents the weighted average of E,F, and G, if point E weighs twice as much as point F and point G weighs three times as much as point F.
Let's say the coordinate of point F is x.
Since E weighs twice as much as F, the coordinate of point E is 2x.
And since G weighs three times as much as F, the coordinate of point G is 3x.
We want to find the weighted average of E, F, and G, so we add up the coordinates and divide by the total weight.
The total weight is found by adding the weights: 1 (for F) + 2 (for E) + 3 (for G) = 6.
The sum of the coordinates is: x + 2x + 3x = 6x.
The weighted average is: (sum of coordinates) / (total weight) = 6x / 6 = x.
Therefore, the coordinate of the point that represents the weighted average of E, F, and G is x.
In other words, the answer is the coordinate of point F, which is represented by x.