b Which SAT score increases at a faster rate? When are the SAT scores the same?
A
a After 7 weeks.
B
b Joman
Practice makes perfect
a Before we can solve the exercise we will introduce a few variables.
x&=number of weeks
y&=SAT score
We know that Jalil's current score is 850, and every week his score rises by 10. With this information we can write an equation that describes Jalil's SAT score.
y=850+10x
Similarly, Joman's current score is 570 and every week it grows by 50 points. With this information, we can write a second equation that describes Joman's SAT score.
y=570+50x
If we combine these equations we get a system of equation which we can solve with the Substitution Method.
After 7 weeks their SAT scores are the same. We do not have to bother solving for y, as we were only asked when their SAT scores are the same.
b From Part A, we know that Joman's and Jalil's score is the same after 7 weeks. Since Joman's score is increasing at a faster rate than Jalil's, we can determine that Joman's SAT score must be higher than Jalil's score after 12 weeks.
