Question

scott and william are reading the same book for their english class. scott is currently on page 150, and william is on page 66. scott reads 10 pages each day, and william reads 22 pages each day. which equation can you use to find d, the number of days it will take for william to have read as many pages as scott? $150 + 22d = 66 + 10d$ $150 + 10d = 66 + 22d$ how many days will it take for william to have read as many pages as scott? days

Explanation:

Part 1: Finding the Correct Equation

To determine the equation, we analyze the number of pages each has read after \( d \) days. Scott starts at page 150 and reads 10 pages per day, so his total pages after \( d \) days is \( 150 + 10d \). William starts at page 66 and reads 22 pages per day, so his total pages after \( d \) days is \( 66 + 22d \). We set these equal when their page counts are the same, giving the equation \( 150 + 10d = 66 + 22d \).

Step 1: Subtract \( 10d \) from both sides

To isolate the terms with \( d \), we subtract \( 10d \) from each side of the equation \( 150 + 10d = 66 + 22d \).
\( 150 + 10d - 10d = 66 + 22d - 10d \)
Simplifying, we get \( 150 = 66 + 12d \).

Step 2: Subtract 66 from both sides

Next, we subtract 66 from both sides to isolate the term with \( d \).
\( 150 - 66 = 66 + 12d - 66 \)
Simplifying, we have \( 84 = 12d \).

Step 3: Divide both sides by 12

To solve for \( d \), we divide both sides of the equation \( 84 = 12d \) by 12.
\( \frac{84}{12} = \frac{12d}{12} \)
Simplifying, we find \( d = 7 \).

Answer:

\( 150 + 10d = 66 + 22d \)

Part 2: Solving for \( d \)