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# Jamie earned 15 more points on her test than Paul earned. Their points added up to 143. How many points did each student earn?

The question is self explanatory....HELP ME!!!!!

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### 4 Answers

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.

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

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

With this,

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

Therefore,

Paul's test score  =   y  =  64

Jamie's test score  =   x  =  y + 15  =  64 + 15  =  79

Two Exams with total score of 143.

Jamie scored 15 points more...therefore 143 minus 15 is where you start to make Jamie = Paul

143-15= 128

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.