Question

Phil and Stacy create repeating patterns using shapes. Phil's rule is "oval, square," and Stacy's rule is "oval, square, circle, oval. If they both have 96 shapes in their pattern, which pattern has more ovals?

A. Phil's pattern has more ovals with 24 ovals.
B. Stacy's pattern has more ovals with 48 ovals.
C. They both have 48 ovals.
D. They both have 24 ovals.

Answer 1

Both Phil and Stacy have 48 ovals in their patterns of 96 shapes. Phil's pattern repeats every two shapes, and Stacy's every four shapes with two ovals in each complete sequence.

Step-by-step explanation:

The student has asked which pattern, between Phil's and Stacy's, has more ovals if they each have 96 shapes in their pattern. To find out, we break down each pattern into their repeating units. Phil's pattern is 'oval, square,' which means that every two shapes in the sequence include one oval. Thus, if Phil has 96 shapes in total, the number of full patterns he can make is 96 divided by 2, which is 48. Therefore, Phil has 48 ovals in his pattern.

Stacy's pattern is 'oval, square, circle, oval,' meaning that every four shapes include two ovals. So, if Stacy has 96 shapes, we can divide 96 by 4 to get the number of full sequences, which is 24, and since each sequence includes two ovals, we multiply 24 by 2 to get 48 ovals as well. Hence, both Phil and Stacy have 48 ovals in their patterns. The correct answer is C: They both have 48 ovals.