The sum of a student's three scores is 220 ect.....

Question

The sum of a student's three scores is 220. If the first is 15 points more than the second, and the sum of the first two is 31 more than twice the third, then what was the first score? Explain how you obtain your answer.

Answer 1

Let the scores be a, b and c. a+b+c=220.

a=b+15, a+b=2c+31, so 2c+31+c=220, 3c=220-31=189, c=189/3=63.

a-b=15 and a+b=2c+31=126+31=157.

a-b+a+b=15+157=172, 2a=172, a=172/2=86 (the first score).