Question

l 6-114 as khan and jomman practice for college entrance tests, their scores increase. khan’s current score is 750 and is rising 8 points per week. jomman’s current score is 650 but is growing by 30 points per week. write an equation or system of equations to determine when jomman will catch up with khan. be sure to define your variable(s).

Explanation:

Step1: Define variables

Let $w$ = number of weeks, $K(w)$ = Khan's score after $w$ weeks, $J(w)$ = Jorman's score after $w$ weeks.

Step2: Write Khan's score equation

Khan starts at 750, gains 8/week:
$K(w) = 750 + 8w$

Step3: Write Jorman's score equation

Jorman starts at 650, gains 30/week:
$J(w) = 650 + 30w$

Step4: Set scores equal (catch up)

Set $K(w) = J(w)$:
$750 + 8w = 650 + 30w$

Step5: Solve for $w$

Subtract $650 + 8w$ from both sides:
$750 - 650 = 30w - 8w$
$100 = 22w$
$w = \frac{100}{22} = \frac{50}{11} \approx 4.55$

Answer:

Define $w$ = number of weeks until Jorman catches up.
The system of equations is:
$K(w) = 750 + 8w$
$J(w) = 650 + 30w$
Set $750 + 8w = 650 + 30w$, solving gives $w = \frac{50}{11}$ (or approximately 4.55 weeks).