Question

8-41. as khalil and jomari practice for the sat, their scores on practice tests rise. khalil’s current score is 850, and it is rising by 10 points per week. on the other hand, jomari’s current score is 570 and is growing by 50 points per week.

a. when will jomari’s score catch up to khalil’s?

b. if the sat test is in 12 weeks, who will score highest?

Explanation:

Step1: Define variables and equations

Let $w$ = number of weeks.
Khalil's score: $S_K = 850 + 10w$
Joman's score: $S_J = 570 + 50w$

Step2: Set scores equal (part a)

Find $w$ when $S_K = S_J$:
$$850 + 10w = 570 + 50w$$

Step3: Solve for $w$ (part a)

Rearrange to isolate $w$:
$$850 - 570 = 50w - 10w$$
$$280 = 40w$$
$$w = \frac{280}{40} = 7$$

Step4: Calculate scores at 12 weeks (part b)

Khalil's score:
$$S_K = 850 + 10(12) = 850 + 120 = 970$$
Joman's score:
$$S_J = 570 + 50(12) = 570 + 600 = 1170$$

Step5: Compare scores (part b)

$1170 > 970$, so Joman's score is higher.

Answer:

a. 7 weeks
b. Joman will score the highest.