QuestionYou start with 60 points, earn 8 points for correct answers, and lose 2 for wrong ones. With 10 questions, you scored 120. How many did you answer correctly?

Studdy Solution

STEP 1

Assumptions1. You get60 points for just taking the test. You get8 points for each correct answer3. You lose points for each wrong answer4. You answered10 questions in total5. Your total score is120 points

STEP 2

First, we need to find the total points earned from answering the questions, which is the total score minus the points for taking the test.
$Points\, from\, answers = Total\, score - Points\, for\, taking\, the\, test$

STEP 3

Now, plug in the given values for the total score and the points for taking the test to calculate the points from answers.
$Points\, from\, answers =120 -60$

STEP 4

Calculate the points from answers.
$Points\, from\, answers =120 -60 =60$

STEP 5

Let's denote the number of correct answers as $x$ and the number of wrong answers as $10 - x$ . We can set up an equation based on the points from answers, where each correct answer gives8 points and each wrong answer loses2 points.
$Points\, from\, answers =8x -2(10 - x)$

STEP 6

Plug in the value for the points from answers.
$60 =8x -2(10 - x)$

STEP 7

implify the equation.
$60 =x -20 +2x$

STEP 8

Combine like terms.
$60 =10x -20$

STEP 9

Add20 to both sides of the equation to isolate the term with $x$ .
$60 +20 =x$

STEP 10

implify the left side of the equation.
$80 =10x$

STEP 11

Finally, divide both sides of the equation by10 to solve for $x$ .
$x =80 /10$

STEP 12

Calculate the value of $x$ .
$x =80 /10 =8$ You got8 questions right.

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QuestionYou start with 60 points, earn 8 points for correct answers, and lose 2 for wrong ones. With 10 questions, you scored 120. How many did you answer correctly?

Studdy Solution

STEP 1

Assumptions1. You get60 points for just taking the test. You get8 points for each correct answer3. You lose points for each wrong answer4. You answered10 questions in total5. Your total score is120 points

STEP 2

First, we need to find the total points earned from answering the questions, which is the total score minus the points for taking the test.
$Points\, from\, answers = Total\, score - Points\, for\, taking\, the\, test$

STEP 3

Now, plug in the given values for the total score and the points for taking the test to calculate the points from answers.
$Points\, from\, answers =120 -60$

STEP 4

Calculate the points from answers.
$Points\, from\, answers =120 -60 =60$

STEP 5

Let's denote the number of correct answers as $x$ and the number of wrong answers as $10 - x$ . We can set up an equation based on the points from answers, where each correct answer gives8 points and each wrong answer loses2 points.
$Points\, from\, answers =8x -2(10 - x)$

STEP 6

Plug in the value for the points from answers.
$60 =8x -2(10 - x)$

STEP 7

implify the equation.
$60 =x -20 +2x$

STEP 8

Combine like terms.
$60 =10x -20$

STEP 9

Add20 to both sides of the equation to isolate the term with $x$ .
$60 +20 =x$

STEP 10

implify the left side of the equation.
$80 =10x$

STEP 11

Finally, divide both sides of the equation by10 to solve for $x$ .
$x =80 /10$

STEP 12

Calculate the value of $x$ .
$x =80 /10 =8$ You got8 questions right.

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QuestionYou start with 60 points, earn 8 points for correct answers, and lose 2 for wrong ones. With 10 questions, you scored 120. How many did you answer correctly?

Studdy Solution

STEP 1

Assumptions1. You get60 points for just taking the test. You get8 points for each correct answer3. You lose points for each wrong answer4. You answered10 questions in total5. Your total score is120 points

STEP 2

STEP 3

Now, plug in the given values for the total score and the points for taking the test to calculate the points from answers.Points from answers=120−60Points\, from\, answers =120 -60Pointsfromanswers=120−60

STEP 4

Calculate the points from answers.Points from answers=120−60=60Points\, from\, answers =120 -60 =60Pointsfromanswers=120−60=60

STEP 5

STEP 6

Plug in the value for the points from answers.60=8x−2(10−x)60 =8x -2(10 - x)60=8x−2(10−x)

STEP 7

implify the equation.60=x−20+2x60 =x -20 +2x60=x−20+2x

STEP 8

Combine like terms.60=10x−2060 =10x -2060=10x−20

STEP 9

Add20 to both sides of the equation to isolate the term with xxx.60+20=x60 +20 =x60+20=x

STEP 10

implify the left side of the equation.80=10x80 =10x80=10x

STEP 11

Finally, divide both sides of the equation by10 to solve for xxx.x=80/10x =80 /10x=80/10

STEP 12

Calculate the value of xxx.x=80/10=8x =80 /10 =8x=80/10=8You got8 questions right.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Now, plug in the given values for the total score and the points for taking the test to calculate the points from answers.
$Points\, from\, answers =120 -60$

Calculate the points from answers.
$Points\, from\, answers =120 -60 =60$

Plug in the value for the points from answers.
$60 =8x -2(10 - x)$

implify the equation.
$60 =x -20 +2x$

Combine like terms.
$60 =10x -20$

Add20 to both sides of the equation to isolate the term with $x$ .
$60 +20 =x$

implify the left side of the equation.
$80 =10x$

Finally, divide both sides of the equation by10 to solve for $x$ .
$x =80 /10$

Calculate the value of $x$ .
$x =80 /10 =8$ You got8 questions right.