The sum of a students three scores is 217. If the first is 30 points more than the the second, and the sum of the first two is 16 more than twice the third, what was the first score?

90

Explanation:

We have three students

Let the score of the First student be represented as = A

Let the score of the Second Student be represented as = B

Let the score of the Third Student be represented as = C

The sum of the three is 217

Therefore:

A+B+C = 217 Equation 1

If the first is 30 points more than the the second

Therefore,

A= 30 + B

A - B = 30 Equation 2

The sum of the first two is 16 more than twice the third

A+B = 16 + 2(C)

A+B = 16 + 2C Equation 3

Therefore substitute 16 + 2C for A+B in Equation 1

A+B+C = 217 Equation 1

Hence, 16+2C+C = 217

16 + 3C = 217

3C = 217 - 16

3C = 201

C = 201 ÷ 3

C = 67

The score of the third(third student) = 67

The next step would be to substitute 67 for C in Equation 1

A+B+C = 217 Equation 1

A+B+ 67 = 217

A+ B = 217 - 67

A+B = 150

A+B = 150 Equation 4

Therefore, we combined Equation 2 and Equation 4

A - B = 30 Equation 2

A+B = 150 Equation 4

We would use the Elimination method

2A = 180

A = 180÷2

A = 90

Therefore the first score (for the first student ) = 90

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