Question

School A and B are competing in an academic contest. at the beginning of the final round, school A has 174 points and school B has 102 points, in the final round, correct answers earn 10 points and incorrect answers loose 6 points. school A hives the same number of correct and incorrect answers during the final round. school B gives no incorrect answers and the same number of correct answers as school A. the contest ends with te two schools tied. which equation models the scoring in the final round and outcome of the contest?

Answer 1

School A gave 12 correct and 12 incorrect answers. School B gave 12 correct answers and the competition was tied.

Explanation:

We are given the following information:

School A points = 174

School B points = 102

Every correct answer is awarded 10 points and every incorrect answer reduces 6 points.

Let x be the number of correct answer given by school A and thus x is the number of incorrect answer given by school A. The, school B also gives x number of correct answer.

Thus, the scored can be modeled with the following equations:

School A:
`174 + 10x - 6x = 174 + 4x`

School B:
`102 + 10x`

Since, both the schools tied, equating both the equations:

`174 + 4x = 102 + 10x\\\Rightarrow 10x - 4x = 174 -102\\\Rightarrow 6x = 72\\\Rightarrow x= 12`

Thus, school A gave 12 correct and 12 incorrect answers. School B gave 12 correct answers and the competition was tied.