Question

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 P represent the number of pages left to read after t hours.

Answer 1

p = 570 - 220

Explanation:

After 4 hours Naoya read 220 pages and had 350 pages left means that there was 570 pages total.

55 x 4 = 220 = 350 + 220 = 570

I'm really sorry if the answer isn't correct, I tried my best to help :(

Hope this helps tho!

Answer 2

Answer:y=−55x+570

Explanation:

Naoya read at a constant rate, so we are dealing with a linear relationship.

Let's interpret the meaning of the given information in terms of the line representing this relationship.

Hint #2

2 / 4

Naoya read at a rate of

5555

55

55

pages per hour. This corresponds to a slope with an absolute value of

5555

55

55

.

Notice that we are interested in the pages left to read. So our line is decreasing, which means the slope is

−55\greenD{-55}

−55

start color #1fab54, minus, 55, end color #1fab54

.

After

44

4

4

hours, he had

350350

350

350

pages left to read. This corresponds to the point

(4,350)(4, 350)

(4,350)

left parenthesis, 4, comma, 350, right parenthesis

.

Hint #3

3 / 4

So the slope of the relationship's line is

−55\greenD{-55}

−55

start color #1fab54, minus, 55, end color #1fab54

and the line passes through

(4,350)(4, 350)

(4,350)

left parenthesis, 4, comma, 350, right parenthesis

.

Let's find the

yy

y

y

-intercept, represented by the point

(0,b)(0, \maroonD b)

(0,b)

left parenthesis, 0, comma, start color #ca337c, b, end color #ca337c, right parenthesis

, using the slope formula:

b−3500−4=−55\dfrac{\maroonD b-350}{0-4}=\greenD{-55}

0−4

b−350

​

=−55

start fraction, start color #ca337c, b, end color #ca337c, minus, 350, divided by, 0, minus, 4, end fraction, equals, start color #1fab54, minus, 55, end color #1fab54

Solving this equation, we get

b=570\maroonD{b=570}

b=570

start color #ca337c, b, equals, 570, end color #ca337c

.

[Show me the solution.]

b−3500−4=−55b−350=−55(−4)b−350=220b=570\begin{aligned} \dfrac{b-350}{0-4}&=-55 \\\\ b-350&=-55(-4) \\\\ b-350&=220 \\\\ b&=570 \end{aligned}

0−4

b−350

​

b−350

b−350

b

​

=−55

=−55(−4)

=220

=570

​

Hint #4

4 / 4

Now we know the slope of the line is

−55\greenD{-55}

−55

start color #1fab54, minus, 55, end color #1fab54

and the

yy

y

y

-intercept is

(0,570)(0, \maroonD{570})

(0,570)

left parenthesis, 0, comma, start color #ca337c, 570, end color #ca337c, right parenthesis

, so we can write the equation of that line:

y=−55x+570y=\greenD{-55} x+\maroonD{570}

y=−55x+570

straight from khan academy