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? $\newline$ Choices: $\newline$ (A) $150 + 22d = 66 + 10d$ $\newline$ (B) $150 + 10d = 66 + 22d$ $\newline$ How many days will it take for William to have read as many pages as Scott? $\newline$ ____ days

Full solution

Q. 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?

\newline

Choices:

\newline

(A)

150 + 22d = 66 + 10d

\newline

(B)

150 + 10d = 66 + 22d

\newline

How many days will it take for William to have read as many pages as Scott?

\newline

____ days

Set Up Equation: Let's set up an equation where the total number of pages read by Scott equals the total number of pages read by William after $d$ days. Scott starts at page $150$ and reads $10$ pages per day, so after $d$ days, he will have read $150 + 10d$ pages. William starts at page $66$ and reads $22$ pages per day, so after $d$ days, he will have read $66 + 22d$ pages. We want to find the value of $d$ when these two expressions are equal.
Write Equation: We can now write the equation as $150 + 10d = 66 + 22d$ . This equation represents the point in time when Scott and William will have read the same number of pages.
Solve for d: To solve for d, we need to get all the d terms on one side and the constants on the other. Let's subtract $10d$ from both sides to get the d terms on one side: $150 + 10d - 10d = 66 + 22d - 10d$ .
Subtract Constants: Simplifying the equation, we get $150 = 66 + 12d$ . Now, let's subtract $66$ from both sides to isolate the term with $d$ : $150 - 66 = 12d$ .
Isolate d Term: Performing the subtraction, we find that $84 = 12d$ . Now, to solve for $d$ , we divide both sides by $12$ : $\frac{84}{12} = d$ .
Divide by $12$ : Calculating the division, we get $7 = d$ . So, it will take William $7$ days to have read as many pages as Scott.