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.
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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.
For Border 1, tulips are added above and below the daisies, which gives a total of 6 tulips. A tulip is then added to the end of each row of daisies, which gives 4 tulips. So, there is a total of
tulips in Border 1.
For Border 2, there are
additional tulips added to the garden plus the 10 original tulips from Border 1.
8 + 10
For Border 3, there are
additional tulips added to the garden plus the 10 original tulips from Border 1 and 8 additional tulips from Border 2.
8(2) + 10
So, the expression for the number of tulips in the garden with Border b is .
