Word problem Help

Question

You have earned a total of 270 points on the three math tests so far this term. The sum of the scores on the first and second tests exceeds the third score by 102 points. Your score on the first test is 6 points less than the score on your second test. Find the three test scores for this term so far.

Answer 1

X+Y+Z = 270

 

X+Y = Z+102

 

X=Y-6

 

Substituting the second equation into the first equation:

  z+102 + z = 270

 

  2z + 102 = 270

  2z = 270 - 102

  2z = 168

 

  z = 84

 

 

The system becomes:

 

 X+Y  = 186

 

X = y-6

 

y-6 + y = 186

 

2y - 6 = 186

 

2y = 192

 

y = 96

 

x = 96-6 = 90

 

Exam 1:90

Exam 2: 96

Exam 3:84

 

 

 

Answer 2

a + b + c = 270 -------> a + b = -c + 270

a + b = c + 102

a = b - 6 ------> a - b = -6

 

If we add the first two equations...

 

2a + 2b = 372

a + b = 186

 

Adding this to the 3rd equation...

 

2a = 180

a = 90

 

90 + b = 186

b = 96

 

186 = -c + 270

c = 84

 

90,96,84