Question

Jerry is planting white daisies and red tulips in his garden and he wants to choose a pattern in which the tulips surround the daisies. He uses tiles to generate patterns starting with two rows of three daisies. He surrounds these daisies with a border of tulips. The design continues as shown. Jerry writes the expression 8(b − 1) + 10 for the number of tulips in each border, wherein b is the border number and b ≥ 1. Complete the explanation to explain why Jerry's expression is correct.

Answer 1

The borders are shown in the picture attached.

As you can see, starting with border 1, we have 6 daises (white squares) surrounded by 10 tulips (colored squares). Through Jerry's expression we expected:
8(b − 1) + 10 =
8(1 − 1) + 10 =
0 + 10 =
10 tulips.

When considering border 2, we expect: 
8(b − 1) + 10 =
8(2 − 1) + 10 =
8 + 10 =
18 tulips.
Indeed, we have the 10 tulips from border 1 and 8 additional tulips, for a total of 18 tulips.

Then, consider border 3, we expect:
8(b − 1) + 10 =
8(3 − 1) + 10 =
16 + 10 =
26 tulips.
Again, this is correct: we have the 10 tulips used in border 1 plus other 16 tulips, for a total of 26.

Therefore, Jerry's expression is correct.