Question

Prerequisite: Relating Patterns Study the example showing how to describe the relationship between two patterns. Then solve problems 1-6. Cost of Cost of Headbands (S) | T-shirts ($) Ordered Pairs Example The school store sells headbands for $2 each and T-shirts for $8 each. Write ordered pairs to compare the cost of headbands to T-shirts for 0, 1, 2,3,4, and 5 of each item. 0 0 (0,0) 2 8 4 16 12,8) (4.16) (6,24) 6 24 8 32 (8,32) Use a table to show the two numerical patterns. 10 40 (10, 40) The cost of headbands follows the rule "add 2." 0,2,4,6,8,10 The cost of T-shirts follows the rule "add 8." 0, 8, 16, 24, 32, 40 Then write the corresponding terms as ordered pairs. 1 Use the rule "add 8" to find the cost of 6 T-shirts. Explain how you found your answer. Vod correspo terms n in the sal or more 2 For each ordered pair in the table, how does the second number compare to the first number? ordered numbers point on plane 3 If the cost of headbands is $20, what is the corresponding cost for T-shirts? Curriculum Associates, LLC Copying is not permitted

Answer 1

We notice that the cost of head bands jump from 0 to 2, then to 4, then to 6, etc in a pattern that is adding 2 units every time.

The cost of T-shirts goes with the "add 8" rule, since each one costs $8.

Then to answer the first question to calculate the price of 6 headbands, we do:

8 + 8 + 8 + 8 + 8 + 8 = 6 * 8 = $48 We notice that we can simply multiply the number of T-shirts needed time the unit price for T-shirts.

Second question: How does the second number on the table of pairs indicating prices of headbands in the first loaction, and prices of T-shirts in the second, compare.

Notice we have the pairs:

(0, 0), (2, 8), (4, 16), (6, 24), (8, 32), and (10, 40)

where we see that the second ordered quantity is always 4 times the first quantity listed.

0 = 0 * 4

8 = 2 * 4

16 = 4 * 4

24 = 6 * 4

32 = 8 * 4

40 = 10 * 4

The second number in the pair is always 4 times the first number in the pair.

Third question: If the cost of headbands is $20, what is the cost of T-shirts?

Since we know that T-shirt prices relate to headband prices via a product times 4, we can say that the price of T-shirts would be $20 * 4 = $80