Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.64.6(13 lesson ratings)(13)
You can use mental math to do the problem.
Taking 15 points away from Jamie's score, then the two should have earned equal points.
Therefore, Paul earned (143-15)/2 = 64 points, and Jamie earned 64+15 = 79 points.
Jean-Guy L. | Experienced Tutor in KentExperienced Tutor in Kent
4.94.9(232 lesson ratings)(232)
Since we don't know the number of points Paul earned, we will call it the variable 'X'. So the problem can described by the following equation:
Number of points of Paul + Number of points of Jamie = 143
X + ( X + 15) = 143, Jamie earned 15 points more than Paul
2X + 15 = 143
2X = 143-15
X= 128/2 = 64, Paul earned 64 points and Jamie earned X+15=79 points
Tamara J. | Math Tutoring - Algebra and Calculus (all levels)Math Tutoring - Algebra and Calculus (al...
4.94.9(51 lesson ratings)(51)
Let Jamie's test score equal x and Paul's test score equal y. The problem states that the total of their test scores combined equals 143. That is, x + y = 143
Since this equation has two unknown variable, we need to substitute one of the variables with an expression that is in terms of the other variable. The problem states that Jamie earned 15 more points on her test than Paul earned on his, which brings us to the following:
Paul's test score = y
Jamie's test score = x ==> x = y + 15
x + y = 143
(y + 15) + y = 143
y + 15 + y = 143
2y + 15 = 143
2y + 15 - 15 = 143 - 15
2y = 128
2y/2 = 128/2
y = 64
Paul's test score = y = 64
Jamie's test score = x = y + 15 = 64 + 15 = 79
Brian B. | Making Math Matter...and Easy to Understand! Making Math Matter...and Easy to Underst...
5.05.0(226 lesson ratings)(226)
Two Exams with total score of 143.
Jamie scored 15 points more...therefore 143 minus 15 is where you start to make Jamie = Paul
Now divide 128 by two to get the points for each Jaime and Paul 128/2 = 64 points each
But Jamie had 15 more, so add them back in to the 64.....64+15 = 79 for Jaime, 64 for Paul.
Algebraically, it looks like 2x+15 = 143, where x represents Paul's score.