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?

(1 point)
Responses

Phil's pattern has more ovals with 24 ovals.

Phil's pattern has more ovals with 24 ovals.

Stacy's pattern has more ovals with 48 ovals.

Stacy's pattern has more ovals with 48 ovals.

They both have 48 ovals.

They both have 48 ovals.

They both have 24 ovals.

They both have 24 ovals.
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Answer 1

To determine how many ovals Phil and Stacy have in their patterns, we need to analyze the repeating patterns.

**Phil's Pattern:**
- The repeating sequence is "oval, square" which contains 1 oval and 1 square.
- Therefore, each complete cycle has 2 shapes (1 oval + 1 square).
- If he has a total of 96 shapes, then the number of complete cycles is:
\[
\frac{96}{2} = 48 \text{ cycles}
\]
- Since each cycle contains 1 oval, the total number of ovals Phil has is:
\[
48 \text{ ovals}
\]

**Stacy's Pattern:**
- The repeating sequence is "oval, square, circle, oval," which contains 2 ovals, 1 square, and 1 circle.
- Therefore, each complete cycle has 4 shapes (2 ovals + 1 square + 1 circle).
- If she has a total of 96 shapes, then the number of complete cycles is:
\[
\frac{96}{4} = 24 \text{ cycles}
\]
- Since each cycle contains 2 ovals, the total number of ovals Stacy has is:
\[
24 \times 2 = 48 \text{ ovals}
\]

Now we can compare the number of ovals:
- Phil has 48 ovals.
- Stacy has 48 ovals.

Therefore, they both have the same number of ovals (48).

So the correct response is:
- **They both have 48 ovals.**