Question

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?

Answer 1

Answer:

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

Answer 2

Answer:

First score is 90

Step-by-step explanation:

Let A represent the first score

Let B represent the second score

Let C represent the third score

A+B+C=217 equation 1

If the first score A is 30 points more than the second,B

A=B-30  equation 2

Lastly,sum of A&B is 16 more than 2C

A+B=2C+16 equation 3

From equation 1

A+B=217-C equation 4

substitute for A+B in equation 3

217-C=2C+16

217-16=2C+C

201=3C

C=67

substituting C in equation 4

A+B=217-67

A+B=150

if the first score more than the first,then the first 90 while second 60 since A+B=150