Carly looked at a map of her neighborhood and saw that the streets form 16 intersections. Some streets on the map were represented by horizontal lines, and some streets were vertical lines. How many streets could there be in Carly's neighborhood?
Chris, Take a sheet of paper and draw a map with 16 intersections. Then count the streets.
Draw four parallel horizontal lines on a piece of paper. Then see how many vertical lines you have to draw to create sixteen intersections.
the answer is 29
To find out how many streets there could be in Carly's neighborhood, we need to consider the number of intersections created by those streets.
Let's first consider the horizontal lines on the map. Each horizontal line can intersect with all the vertical lines on the map, creating intersections. If there are n horizontal lines, they can form n intersections with each vertical line. So, the number of intersections created by horizontal lines is equal to the number of horizontal lines multiplied by the number of vertical lines.
Similarly, each vertical line can intersect with all the horizontal lines on the map. If there are m vertical lines, they can form m intersections with each horizontal line. Again, the number of intersections created by vertical lines is equal to the number of vertical lines multiplied by the number of horizontal lines.
Since the total number of intersections is given as 16, we can set up an equation:
n * m = 16
We need to find all the possible combinations of n and m (where n and m are whole numbers) that satisfy this equation.
Let's list the factors of 16, which are pairs of numbers that multiply together to give 16:
1 * 16 = 16
2 * 8 = 16
4 * 4 = 16
8 * 2 = 16
16 * 1 = 16
From this list, we can see that there are five possible combinations of n and m that satisfy the equation. These combinations are: (1, 16), (2, 8), (4, 4), (8, 2), and (16, 1).
Therefore, Carly's neighborhood could have different configurations of streets, such as 17 streets when there is 1 horizontal and 16 vertical, or 10 streets when there are 2 horizontal and 8 vertical, or 8 streets when there are 4 horizontal and 4 vertical, and so on.