$1$ . As Jhalil and Joman practice for the SAT, their scores on practice tests rise. Jhalil's current score is $850$ , and it is rising by $10$ points per week. On the other hand, Joman's current score is $570$ and is growing by $50$ points per week. $\newline$ a. When will Joman's score catch up to Jhalil's? $\newline$ b. If the SAT test is in $12$ weeks, who will score highest?

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1

. As Jhalil and Joman practice for the SAT, their scores on practice tests rise. Jhalil's current score is

850

, and it is rising by

10

points per week. On the other hand, Joman's current score is

570

and is growing by

50

points per week.

\newline

a. When will Joman's score catch up to Jhalil's?

\newline

b. If the SAT test is in

12

weeks, who will score highest?

Set Equations: Let's denote Jhalil's score as $Jh$ and Joman's score as $Jo$ . We can write two equations based on the information given: $\newline$ $Jh = 850 + 10t$ $\newline$ $Jo = 570 + 50t$ $\newline$ where $t$ is the number of weeks. $\newline$ We want to find out when $Jo$ will be equal to $Jh$ .
Solve for t: To find when Joman's score will catch up to Jhalil's, we set the two equations equal to each other: $\newline$ $850 + 10t = 570 + 50t$ $\newline$ Now we solve for $t$ .
Calculate Scores: Subtract $10t$ from both sides of the equation: $\newline$ $850 = 570 + 40t$ $\newline$ Now subtract $570$ from both sides: $\newline$ $280 = 40t$
Compare Scores: Divide both sides by $40$ to solve for $t$ : $\newline$ $t = \frac{280}{40}$ $\newline$ $t = 7$ $\newline$ So, Joman will catch up to Jhalil in $7$ weeks.
Compare Scores: Divide both sides by $40$ to solve for $t$ : $t = \frac{280}{40}$ $t = 7$ So, Joman will catch up to Jhalil in $7$ weeks.Now let's calculate the scores after $12$ weeks to see who will have the higher score. $\newline$ For Jhalil: $Jh = 850 + 10 \times 12$ $Jh = 850 + 120$ $Jh = 970$
Compare Scores: Divide both sides by $40$ to solve for $t$ : $t = \frac{280}{40}$ $t = 7$ So, Joman will catch up to Jhalil in $7$ weeks.Now let's calculate the scores after $12$ weeks to see who will have the higher score. $\newline$ For Jhalil: $Jh = 850 + 10 \times 12$ $Jh = 850 + 120$ $Jh = 970$ For Joman: $Jo = 570 + 50 \times 12$ $Jo = 570 + 600$ $Jo = 1170$
Compare Scores: Divide both sides by $40$ to solve for $t$ : $t = \frac{280}{40}$ $t = 7$ So, Joman will catch up to Jhalil in $7$ weeks.Now let's calculate the scores after $12$ weeks to see who will have the higher score. $\newline$ For Jhalil: $Jh = 850 + 10 \times 12$ $Jh = 850 + 120$ $Jh = 970$ For Joman: $Jo = 570 + 50 \times 12$ $Jo = 570 + 600$ $Jo = 1170$ Comparing the scores after $12$ weeks, Joman will have a higher score than Jhalil.