The sum of a students three scores is 216. The first is 11 more than the second,

Question

The sum of a students three scores is 216. The first is 11 more than the second, and the sum of the first two is 15 more than twice the third. Find the students first score. The sum of a students three scores is 216. The first is 11 more than the second, and the sum of the first two is 15 more than twice the third. Find the students first score. The sum of a students three scores is 216. The first is 11 more than the second, and the sum of the first two is 15 more than twice the third. Find the students first score. The sum of a students three scores is 216. The first is 11 more than the second, and the sum of the first two is 15 more than twice the third. Find the students first score.

Explanation / Answer

Let the three scores be a,b and c.

Given:

a + b + c = 216 => a + b = 216 - c.

a = b + 11 => a - b = 11.

a + b = 15 + 2c.

From the first and third equations, we have

216 - c = 15 + 2c

=> 216 + 15 = 2c + c

=> 231 = 3c

=> c = 231/3

=> c = 77.

Substituting in the first equation

=> a + b = 216 - 77 = 139.

Adding with second equation

=> (a + b) + (a - b) = 139 + 11

=> 2a = 150

=> a = 150/2 = 75

Substituting in the first equation

=> 75 + b = 139

=> b = 139 - 75 = 64

The student's first score is 75.

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