Question

1. two students are reading a book. keith reads 6 pages a day. tameka reads 5 pages a day, but he starts sooner and has already read 15 pages. part a write a system of equations to represent the situation, using d for days and p for pages. part b graph the system of equations. graph with p (number of pages) on y - axis (0,20,40,60,80,100) and d (day number) on x - axis (0,5,10,15,20) part c will keith and tameka ever be on the same page on the same day? explain.

Explanation:

Part A

Step1: Define variables

Let \( d \) be the number of days and \( p \) be the number of pages.

Step2: Keith's equation

Keith reads 6 pages per day, so the number of pages \( p \) he reads in \( d \) days is \( p = 6d \).

Step3: Tameka's equation

Tameka reads 5 pages per day and has already read 15 pages, so the number of pages \( p \) she reads in \( d \) days is \( p = 5d + 15 \).

Part B

Step1: Find points for Keith's line

Using \( p = 6d \), substitute \( d = 0, 5, 10 \) to get corresponding \( p \) values.

Step2: Find points for Tameka's line

Using \( p = 5d + 15 \), substitute \( d = 0, 5, 10 \) to get corresponding \( p \) values.

Step3: Plot and draw lines

Plot the points for each equation on the given graph (with \( d \) on the x - axis and \( p \) on the y - axis) and draw straight lines through them.

Part C

Step1: Set equations equal

To find when they have read the same number of pages, set \( 6d=5d + 15 \).

Step2: Solve for \( d \)

Subtract \( 5d \) from both sides: \( 6d-5d=5d + 15-5d \), so \( d = 15 \).

Step3: Find \( p \)

Substitute \( d = 15 \) into \( p = 6d \), \( p=6\times15 = 90 \). So on day 15, both will have read 90 pages.

Answer:

\( p = 6d \) (for Keith), \( p = 5d + 15 \) (for Tameka)