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Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read.
Let
y represent the number of pages left to read after
x hours.
Complete the equation for the relationship between the number of pages left and number of hours.

y=

Naoya read a book cover to cover in a single session, at a rate of $55$ pages per hour. After $4$ hours, he had $350$ pages left to read. $\newline$ Let $y$ represent the number of pages left to read after $x$ hours. $\newline$ Complete the equation for the relationship between the number of pages left and number of hours. $\newline$ $y=$

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Write a linear function: word problems

Full solution

Q. Naoya read a book cover to cover in a single session, at a rate of

55

pages per hour. After

4

hours, he had

350

pages left to read.

\newline

Let

y

represent the number of pages left to read after

x

hours.

\newline

Complete the equation for the relationship between the number of pages left and number of hours.

\newline

y=

Calculate total pages read: Determine the total number of pages Naoya read in $4$ hours. $\newline$ Naoya reads at a rate of $55$ pages per hour. To find out how many pages he read in $4$ hours, we multiply the rate by the time. $\newline$ Pages read in $4$ hours = Rate $\times$ Time $\newline$ Pages read in $4$ hours = $55$ pages/hour $\times$ $4$ hours $\newline$ Pages read in $4$ hours = $55$ $0$ pages
Determine initial total pages: Determine the initial total number of pages in the book. $\newline$ We know that after reading for $4$ hours, Naoya had $350$ pages left. Since he read $220$ pages in those $4$ hours, we add the pages read to the pages left to find the initial total number of pages. $\newline$ Initial total number of pages $=$ Pages read in $4$ hours $+$ Pages left after $4$ hours $\newline$ Initial total number of pages $=$ $220$ pages $+$ $350$ pages $\newline$ Initial total number of pages $=$ $570$ pages
Write equation for pages left: Write the equation for the number of pages left after $x$ hours. $\newline$ Let $y$ represent the number of pages left to read after $x$ hours. Since Naoya reads $55$ pages per hour, the number of pages he reads after $x$ hours is $55x$ . To find the number of pages left, we subtract the pages read from the initial total number of pages. $\newline$ Number of pages left after $x$ hours = Initial total number of pages - Pages read after $x$ hours $\newline$ $y = 570 - 55x$

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