Question

6-25. as sally and george practice for the sat, their scores on practice tests rise. sally’s current score is 850, and it is rising by 10 points per week. on the other hand, george’s current score is 570 and is growing by 50 points per week.
a. when will george’s score catch up to sally’s?
b. if the sat test is in 12 weeks, who will score highest?

Explanation:

Step1: Define variables for weeks

Let $w$ = number of weeks from now.

Step2: Write score equations

Sally's score: $S(w) = 850 + 10w$
George's score: $G(w) = 570 + 50w$

Step3: Set scores equal (catch up)

$850 + 10w = 570 + 50w$

Step4: Solve for $w$

$850 - 570 = 50w - 10w$
$280 = 40w$
$w = \frac{280}{40} = 7$

Step5: Calculate scores at 12 weeks

Sally's score: $S(12) = 850 + 10(12) = 850 + 120 = 970$
George's score: $G(12) = 570 + 50(12) = 570 + 600 = 1170$

Answer:

a. George's score will catch up to Sally's in 7 weeks.
b. George will score highest on the SAT in 12 weeks.