+23252 Problem #1:
Let n be the picture number: 1, 2, 3, ...
Let T be the number of tiles: 3, 6, 9, ...
What number times n will have the value T?
-- What number times 1 (for n) will give you 3 (for T)?
-- What number times 2 (for n) will give you 6 (for T)?
-- What number times 3 (for n) will give you 9 (for T)?
This is how you get the formula: T = 3·n
+934 I'm not sure what you're missing here. What times 1 equals 3, what times 2 equals 6, or what times 3 equals 9?
EDIT: I see that Geno has already explained it...can you clarify what you're not understanding?
+167 What number times 1 (for n) will give you 3 (for T)?
1 times 3
What number times 2 (for n) will give you 6 (for T)?
2 times 6
What number times 3 (for n) will give you 9 (for T)?
3 times 9?????????????
+934 The number is 3, 3 times 1 equals 3, 3 times 2 equals 6, 3 times 3 equals 9.
+934 That's the problem, your book might have a different form of answeres that we can provide. Like Geno said, if T is the number of tiles and n is the figure number, then your algebraic expression will be T = 3 * n. The only problem is WE assigned the varibles, not the problem so I'm not sure how your book wants us to show the answer.
+23252 Problem #2:
How to draw the next picture.
-- Notice that the number of tiles in the bottom row of figure 1 is 3
and the number of tiles in the bottom row of figure 2 is 5
and the number of tiles in the bottom row of figure 3 is 7
Using this same pattern, how many tiles will be in the bottom row of figure 4?
How many tiles will be in the bottom row of figure 5?
-- Notice that the number of tiles in the second to the bottom row of figure 1 is 2
and the number of tiles in this row of figure 2 is 4
and the number of tiles in this row of figure 3 is 6.
Using this same pattern, how many tiles will be in this row in figure 4?
How many tiles will be in this row in figure 5?
-- Notice that the number of tiles in the third to the bottom row of figure 1 is 1
and the number of tiles in this row of figure 2 is 3
and the number of tiles in this row of figure 3 is 5.
Using this same pattern, how many tiles will be in this row in figure 4?
How many tiles will be in this row in figure 5?
-- Notice that there is 1 tile sitting on top of the figure in figure 1
and the number of tiles sitting on top of the figure in figure 2 is 2 (2 tiles, one on top of the other.)
and the number of tiles sitting on top of the figure in figure 3 is 3. (3 tiles, one on top of the other.)
Using this pattern, how many tiles will be sitting on top of the figure in figure 4?
How many tiles will be sitting on top of the figure in figure 5?
To create a pattern rule for T (the number of tiles) and n (which figure)
When n = 1, T = 7 (there are 7 tiles in figure 1)
When n = 2, T = 14 (there are 14 tiles in figure 2)
When n = 3, T = 21 (there are 21 tiles in figure 3)
So to find the formula, what number do you have to multiply times n to get the answer for T?
That's how you get the formula: T = 7n.
To predict the number of tiles in figure 10, replace n with 10, and multiply.
