Maths-

General

Easy

Question

# 37. In an academic contest correct answers earn 12 points and incorrect answers lose 5

points. In the final round, school A starts with 165 points and gives the same number

of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.

i)Which equation models the scoring in the final round and the outcome of the contest

- 12x+5x -165 = -12x+65
- 12x-5x +165 = 12x +65
- 5x-12x+165 = 12x +65
- 12x-5x- 165 = 12x +65

Hint:

### Form equation using the given information.

○ Take the variable value as x or any alphabet.

## The correct answer is: 12x-5x +165 = 12x +65

### Answer:

- Step by step explanation:

○ Given:

correct answer = 12 points

incorrect answers = -5 points

School A starts with 165 points and gives the same number of correct and incorrect answers.

School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A

○ Step 1:

○ Let the number of correct answers given by school A be x.

So, the number of incorrect answers is also x.

At school A starts with 165 points. After giving x correct and a incorrect answers points will be

165 + 12x - 5x

School B starts with 65 points. Schools are given the same number of correct answers as school A and no incorrect answers. So, their points will be

65 + 12x

○ Step 2:

○ As both schools tied

∴ 165 + 12x - 5x = 65 + 12x

- Final Answer:

Correct option:

Option B. 165 + 12x - 5x = 65 + 12x

○ Step 2:

○ As both schools tied

∴ 165 + 12x - 5x = 65 + 12x

A symbol (usually a letter) in algebra represents an unknown numerical value in an algebraic expression or an equation. A variable is a non-fixed quantity that can be changed. Variables are essential because they are a significant component of algebra.

¶**Different Types of Variables**

Dependent Variables: The variables whose values are determined by another variable's quantity.

¶Unrelated Variables: The values of an independent variable in an algebraic equation are unaffected by changes. Suppose an algebraic equation has two variables, x and y, and each x value is related to any other y value. In that case, x is an independent variable, and y is a dependent variable.

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