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Simora [160]
2 years ago
6

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 1

6 more than twice the third, what was the first score?
Mathematics
2 answers:
meriva2 years ago
7 0

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

nekit [7.7K]2 years ago
3 0

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

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