Question

name
topic 5
assessment
form b

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.
part c
will keith and tameka ever be on the
same page on the same day? explain.

1. how many solutions does the system

of equations have?
a no solution
b one solution: x = 0, y = 0
c one solution: x = 0, y = 5
d infinitely many solutions

1. taxi a charges a fee of $3.50, plus

$1.75 per mile. taxi b charges a fee
of $1.25, plus $2.00 per mile. at
what distance would the taxis cost
the same?
a 2 miles
b 5 miles
c 9 miles
d 15 miles

1. solve the system of equations. how

many solutions does the system have?
6x + 3y = 24
y = -2x + 8
a no solution
b one solution: x = 2, y = 4
c one solution: x = 3, y = 2
d infinitely many solutions

Explanation:

Question 1 Part A

Step1: Define Keith's equation

Keith reads 6 pages a day, so his total pages \( p \) after \( d \) days is \( p = 6d \).

Step2: Define Tameka's equation

Tameka reads 5 pages a day but has already read 15 pages, so her equation is \( p = 5d + 15 \).

Step1: Analyze the lines' slopes

The two lines in the graph have the same slope (since they are parallel? Wait, no, looking at the graph, wait, actually, if two lines are parallel, they have no solution. Wait, the graph shows two lines with the same slope (since they are parallel) and different y-intercepts. So a system of linear equations with the same slope and different y-intercepts has no solution.

Step2: Match with options

Option A says no solution, which matches.

Step1: Define cost equations

Let \( m \) be miles. Taxi A: \( C_A = 3.50 + 1.75m \), Taxi B: \( C_B = 1.25 + 2.00m \).

Step2: Set costs equal

Set \( 3.50 + 1.75m = 1.25 + 2.00m \).

Step3: Solve for m

Subtract \( 1.75m \) and 1.25: \( 3.50 - 1.25 = 2.00m - 1.75m \) → \( 2.25 = 0.25m \) → \( m = \frac{2.25}{0.25} = 9 \)? Wait, no, wait: \( 3.50 - 1.25 = 2.25 \), \( 2.00m - 1.75m = 0.25m \), so \( m = 2.25 / 0.25 = 9 \)? Wait, but option C is 9 miles. Wait, let's recalculate:

\( 3.50 + 1.75m = 1.25 + 2m \)

Subtract \( 1.75m \) from both sides: \( 3.50 = 1.25 + 0.25m \)

Subtract 1.25: \( 2.25 = 0.25m \)

Divide by 0.25: \( m = 9 \). So option C.

Answer:

The system of equations is \(

$$\begin{cases} p = 6d \\ p = 5d + 15 \end{cases}$$

\)

Question 2