Exercise 25 Page 201

In order to find who, Julio or Jake, will have more pages left to read after 5 days of reading, let's write the equations for each of them. Then, we can use these equations to find the number of pages left.

Jake

Let's write the equation in slope-intercept form. Jake is reading a 168-page book. This value represents the number of pages left to read on day 0. In other words, it's the value of y-intercept. b=168 Also, Jake is reading his book at a rate of 24 pages per day. This means that, after each day of reading, the number of pages left to read decreases by 24. This is our slope. m=- 24Now, we can write the equation that describes this situation. y=- 24x+168 To calculate how many pages Jake will have left to read, we can substitute 5 for x.

y=- 24x+168

Substitute

x= 5

y=- 24* 5+168

Multiply

Multiply

y=- 120+168

AddTerms

Add terms

y=48

Jake will have 48 pages left to read after 5 days of reading.

Julio

We can write the second equation in a similar manner. Let's start with calculating the slope. We know that Julio's reading rate is 1 14 times Jake's rate. We can multiply it by - 24, Jake's rate of reading to find the slope of Julio's equation.

Julio's rate=1 14 *(-24)

MixedToFrac

a bc=a* c+b/c

Julio's rate=5/4* (- 24)

MoveRightFacToNum

a/c* b = a* b/c

Julio's rate=-120/4

CalcQuot

Calculate quotient

Julio's rate=-30

Thus, the slope for Julio's equation is -30. We are also given that Julio's book is 180 pages long. Using the same reasoning as with Jake, we get that b=180. Now we have enough information to write the equation. y=- 30x+180 Substituting x with 5, we can calculate the number of pages left on day 5.

y=- 30x+180

Substitute

x= 5

y=- 30* 5+180

Multiply

Multiply

y=- 150+180

AddTerms

Add terms

y=30

There will be 30 pages left for Julio to read.

Compare

Putting it all together, we have that, after 5 days of reading, Jake will have 48 pages left to read and Julio will have 30 pages left. Therefore, Jake will have more pages to read. Let's calculate the difference between these values. 48-30=18 Jake will have 18 pages more to read that Julio.