QuestionScott is on page 150, William on page 66. They read 10 and 22 pages daily. Find $d$ such that $150 + 10d = 66 + 22d$ . How many days until William catches up?

Studdy Solution

STEP 1

Assumptions1. Scott is currently on page150. William is currently on page663. Scott reads10 pages each day4. William reads22 pages each day5. We are looking for the number of days it will take for William to have read as many pages as Scott

STEP 2

We need to set up an equation that represents the situation. The equation should represent the fact that after $d$ days, the number of pages read by Scott and William will be the same.
The number of pages read by Scott after $d$ days will be his current page count plus the product of the number of pages he reads per day and the number of days. Similarly, the number of pages read by William will be his current page count plus the product of the number of pages he reads per day and the number of days.
So, the equation will be $Scott's\, current\, page\, count + (Scott's\, pages\, per\, day \\times d) = William's\, current\, page\, count + (William's\, pages\, per\, day \\times d)$

STEP 3

Now, plug in the given values for Scott's current page count, Scott's pages per day, William's current page count, and William's pages per day.
$150 + (10 \\times d) =66 + (22 \\times d)$

STEP 4

This simplifies to $150 +10d =66 +22d$ So, the correct equation to use to find $d$ , the number of days it will take for William to have read as many pages as Scott, is $150 +10d =66 +22d$ .

STEP 5

To solve for $d$ , we first need to get all terms involving $d$ on one side of the equation and the constants on the other side. We can do this by subtracting $10d$ from both sides of the equation and subtracting $66$ from both sides of the equation.
$150 +10d -10d -66 =66 +22d -10d -66$

STEP 6

This simplifies to $84 =12d$

STEP 7

Finally, to solve for $d$ , we divide both sides of the equation by $12$ .
$d =84 /12$

STEP 8

Calculate the value of $d$ .
$d =84 /12 =7$ So, it will take7 days for William to have read as many pages as Scott.

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QuestionScott is on page 150, William on page 66. They read 10 and 22 pages daily. Find $d$ such that $150 + 10d = 66 + 22d$ . How many days until William catches up?

Studdy Solution

STEP 1

Assumptions1. Scott is currently on page150. William is currently on page663. Scott reads10 pages each day4. William reads22 pages each day5. We are looking for the number of days it will take for William to have read as many pages as Scott

STEP 2

STEP 3

Now, plug in the given values for Scott's current page count, Scott's pages per day, William's current page count, and William's pages per day.
$150 + (10 \\times d) =66 + (22 \\times d)$

STEP 4

This simplifies to $150 +10d =66 +22d$ So, the correct equation to use to find $d$ , the number of days it will take for William to have read as many pages as Scott, is $150 +10d =66 +22d$ .

STEP 5

To solve for $d$ , we first need to get all terms involving $d$ on one side of the equation and the constants on the other side. We can do this by subtracting $10d$ from both sides of the equation and subtracting $66$ from both sides of the equation.
$150 +10d -10d -66 =66 +22d -10d -66$

STEP 6

This simplifies to $84 =12d$

STEP 7

Finally, to solve for $d$ , we divide both sides of the equation by $12$ .
$d =84 /12$

STEP 8

Calculate the value of $d$ .
$d =84 /12 =7$ So, it will take7 days for William to have read as many pages as Scott.

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QuestionScott is on page 150, William on page 66. They read 10 and 22 pages daily. Find ddd such that 150+10d=66+22d150 + 10d = 66 + 22d150+10d=66+22d. How many days until William catches up?

Studdy Solution

STEP 1

Assumptions1. Scott is currently on page150. William is currently on page663. Scott reads10 pages each day4. William reads22 pages each day5. We are looking for the number of days it will take for William to have read as many pages as Scott

STEP 2

STEP 3

Now, plug in the given values for Scott's current page count, Scott's pages per day, William's current page count, and William's pages per day.150+(10timesd)=66+(22timesd)150 + (10 \\times d) =66 + (22 \\times d)150+(10timesd)=66+(22timesd)

STEP 4

This simplifies to150+10d=66+22d150 +10d =66 +22d150+10d=66+22dSo, the correct equation to use to find ddd, the number of days it will take for William to have read as many pages as Scott, is 150+10d=66+22d150 +10d =66 +22d150+10d=66+22d.

STEP 5

STEP 6

This simplifies to84=12d84 =12d84=12d

STEP 7

Finally, to solve for ddd, we divide both sides of the equation by 121212.d=84/12d =84 /12d=84/12

STEP 8

Calculate the value of ddd.d=84/12=7d =84 /12 =7d=84/12=7So, it will take7 days for William to have read as many pages as Scott.

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QuestionScott is on page 150, William on page 66. They read 10 and 22 pages daily. Find $d$ such that $150 + 10d = 66 + 22d$ . How many days until William catches up?

Now, plug in the given values for Scott's current page count, Scott's pages per day, William's current page count, and William's pages per day.
$150 + (10 \\times d) =66 + (22 \\times d)$

This simplifies to $150 +10d =66 +22d$ So, the correct equation to use to find $d$ , the number of days it will take for William to have read as many pages as Scott, is $150 +10d =66 +22d$ .

This simplifies to $84 =12d$

Finally, to solve for $d$ , we divide both sides of the equation by $12$ .
$d =84 /12$

Calculate the value of $d$ .
$d =84 /12 =7$ So, it will take7 days for William to have read as many pages as Scott.