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Question
keona and ethan write poetry in english class. keona writes 8 lines of poetry. ethan writes 2 times as many lines of poetry as keona. how many lines of poetry does ethan write? \\(\\) let \\( p \\) stand for the number of lines of poetry ethan writes. which bar model represents the problem? \\(\\) keona \\(\boxed{p}\\) ethan \\(\boxed{p}\\ \boxed{p}\\) \\(\overline{\quad 8 \quad}\\) ethan \\(\boxed{8}\\) keona \\(\boxed{8}\\ \boxed{8}\\) \\(\overline{\quad p \quad}\\) ethan \\(\boxed{p}\\) keona \\(\boxed{p}\\ \boxed{p}\\) \\(\overline{\quad 8 \quad}\\) keona \\(\boxed{8}\\) ethan \\(\boxed{8}\\ \boxed{8}\\) \\(\overline{\quad p \quad}\\)
Part 1: How many lines of poetry does Ethan write?
Step1: Identify the relationship
Ethan writes 2 times as many lines as Keona. Keona writes 8 lines. So we need to multiply Keona's lines by 2.
Step2: Calculate Ethan's lines
The formula is \( p = 2\times8 \). Calculating that, \( 2\times8 = 16 \).
Keona writes 8 lines, Ethan writes twice as many (so Ethan's amount is \( p \), and it should be represented as two times Keona's 8 - or in bar model terms, Keona has one bar (8), Ethan has two bars (or a bar equal to two times Keona's). Let's analyze each:
- First model: Keona is \( p \), Ethan is \( p + p \), with total 8? No, Keona's lines are 8, not \( p \).
- Second model: Ethan has 8, Keona has two 8s, which is wrong.
- Third model: Ethan has \( p \), Keona has \( p + p \), with total 8? No, Keona's lines are 8, so if Keona is \( p + p \), then \( p + p=8 \), so \( p = 4 \), which is wrong.
- Fourth model: Keona has 8 (one bar), Ethan has two bars of 8 (so \( p=8 + 8=16 \)), which matches Ethan writing twice as many as Keona (Keona:8, Ethan:16).
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Ethan writes 16 lines of poetry.