Question

monica and sean are both knitting scarves for mother’s day. monica has completed 16 inches of her scarf, and she will knit an additional 10 inches each day. sean is just starting his scarf, and he will knit 14 inches each day. which equation can you use to find d, the number of days it will take for sean’s scarf to be the same length as monica’s? 16 + 10d = 14d 16d + 10 = 14d how long will it take for sean’s scarf to be the same length as monica’s? \boxed{} days

Explanation:

Part 1: Choosing the Correct Equation

Step1: Analyze Monica's Scarf Length

Monica starts with 16 inches and knits 10 inches per day. So after \( d \) days, her length is \( 16 + 10d \).

Step2: Analyze Sean's Scarf Length

Sean starts with 0 inches and knits 14 inches per day. So after \( d \) days, his length is \( 14d \).

Step3: Set Up the Equation

We want when their lengths are equal, so \( 16 + 10d = 14d \).

Step1: Subtract \( 10d \) from Both Sides

\( 16 + 10d - 10d = 14d - 10d \) simplifies to \( 16 = 4d \).

Step2: Divide Both Sides by 4

\( \frac{16}{4} = \frac{4d}{4} \), which gives \( d = 4 \).

Answer:

\( 16 + 10d = 14d \)

Part 2: Solving for \( d \)