Question

solve the problems:
1 what rule could be used to create the pattern 9, 18, 27, 36, 45, 54, ...?
a multiply each term by 2 to get the next term
b multiply each term by 9 to get the next term
c add 9 to get the next term
d add 3 to get the next term
2 look at the patterns below. choose true or false for each statement.
pattern a: 3, 6, 9, 12, 15, 18, ...
pattern b: 18, 36, 54, 72, 90, 108, ...
a. the rule for pattern a is \multiply by 2.\ true false
b. the rule for pattern b is \add 18.\ true false
c. each term in pattern a is 6 times the corresponding term in pattern b. true false
d. each term in pattern b is 3 times the corresponding term in pattern a. true false
3 tickets at a play cost $2 for students and $8 for adults. jason creates two patterns to compare the costs. he writes ordered pairs in the form (student cost, adult cost) for the corresponding numbers of tickets. which ordered pair could be on jasons list of ordered pairs? circle the letter for all that apply.
a (8, 2)
b (10, 40)
c (4, 10)
d (10, 16)
e (6, 24)

Explanation:

Step1: Analyze the first pattern 9, 18, 27, 36, 45, 54,...

• For option A: \(9\times2 = 18\), \(18\times2=36

eq27\).

• For option B: \(9\times9 = 81

eq18\).

• For option C: \(9 + 9=18\), \(18+9 = 27\), \(27+9=36\), \(36 + 9=45\), \(45+9=54\).
• For option D: \(9+3=12

eq18\).

Step2: Analyze Pattern A: 3, 6, 9, 12, 15, 18,...

• The rule is \(n+3\) (where \(n\) is the previous term), not multiply by 2. So for statement a: False.

Step3: Analyze Pattern B: 18, 36, 54, 72, 90, 108,...

• The rule is \(n + 18\). So for statement b: True.

Step4: Compare terms of Pattern A and Pattern B

• \(3\times6=18\), \(6\times6 = 36\), \(9\times6=54\), \(12\times6=72\), \(15\times6=90\), \(18\times6=108\). So each term in Pattern B is 6 times the corresponding term in Pattern A. So statement c: False, statement d: True.

Step5: Analyze ordered - pairs for ticket cost

• Let the number of student tickets be \(x\) and adult tickets be \(y\). The cost for students is \(C_s=2x\) and for adults is \(C_a = 8y\). The ordered pair is \((2x,8y)\).
• For option A: If \(2x = 8\) then \(x = 4\), if \(8y=2\) then \(y=\frac{1}{4}\) (not a whole number of tickets).
• For option B: If \(2x = 10\) then \(x = 5\), if \(8y=40\) then \(y = 5\).
• For option C: If \(2x=4\) then \(x = 2\), if \(8y = 10\) then \(y=\frac{5}{4}\) (not a whole number of tickets).
• For option D: If \(2x=10\) then \(x = 5\), if \(8y=16\) then \(y = 2\).
• For option E: If \(2x=6\) then \(x = 3\), if \(8y=24\) then \(y = 3\).

Answer:

1. C. add 9 to get the next term
2. a. False; b. True; c. False; d. True
3. B. (10, 40); D. (10, 16); E. (6, 24)