Math / Algebra

QuestionSelect the correct answer from each drop-down menu.
Desiree is given an aptitude test with 50 multiple-choice questions. For every correct answer, Desiree will get 3 points. For every wrong answer, 1 point will be deducted. For every question unanswered, 0.5 point is deducted. Desiree did not leave any question unanswered and gets 110 points on the test.
If $x$ is the number of questions Desiree answered correctly, then the equation that represents the given situation is the equation will have $\square$

Studdy Solution

STEP 1

What is this asking? We need to figure out how many questions Desiree got right on her test, given that she got a total of 110 points, with 3 points for correct answers and -1 point for incorrect answers. Watch out! It's easy to mess up the signs when setting up the equation.
Make sure you're adding points for correct answers and subtracting for incorrect ones!
Also, remember there were no unanswered questions.

STEP 2

1. Set up the equation
2. Simplify and solve

STEP 3

Let $x$ be the number of questions Desiree answered correctly.
Since there are 50 total questions and she answered all of them, the number of questions she answered incorrectly is $50 - x$ .

STEP 4

Desiree gets 3 points for each correct answer, so she gets $3 \cdot x$ points from correct answers.
She loses 1 point for each incorrect answer, so she loses $1 \cdot (50 - x)$ points from incorrect answers.
Her total score is the sum of these two values, which we know is 110.

STEP 5

So, the equation representing the situation is: $3x - (50 - x) = 110$

STEP 6

Distribute the negative sign in front of the parentheses: $3x - 50 + x = 110$ We do this because subtracting a quantity is the same as adding its opposite.

STEP 7

Combine the $x$ terms on the left side: $4x - 50 = 110$ We're combining like terms to simplify the equation and make it easier to solve for $x$ .

STEP 8

Add 50 to both sides of the equation: $4x - 50 + 50 = 110 + 50$ $4x = 160$ We add 50 to both sides to isolate the term with $x$ .
We're trying to get $x$ by itself!

STEP 9

Divide both sides by 4: $\frac{4x}{4} = \frac{160}{4}$ $x = 40$ We divide by 4 to get the value of a single $x$ .

STEP 10

Desiree answered 40 questions correctly.
The equation representing the situation is $3x - (50 - x) = 110$ .

Was this helpful?

Studdy Solution

STEP 1

STEP 2

1. Set up the equation
2. Simplify and solve

STEP 3

Let $x$ be the number of questions Desiree answered correctly.
Since there are 50 total questions and she answered all of them, the number of questions she answered incorrectly is $50 - x$ .

STEP 4

Desiree gets 3 points for each correct answer, so she gets $3 \cdot x$ points from correct answers.
She loses 1 point for each incorrect answer, so she loses $1 \cdot (50 - x)$ points from incorrect answers.
Her total score is the sum of these two values, which we know is 110.

STEP 5

So, the equation representing the situation is: $3x - (50 - x) = 110$

STEP 6

Distribute the negative sign in front of the parentheses: $3x - 50 + x = 110$ We do this because subtracting a quantity is the same as adding its opposite.

STEP 7

Combine the $x$ terms on the left side: $4x - 50 = 110$ We're combining like terms to simplify the equation and make it easier to solve for $x$ .

STEP 8

Add 50 to both sides of the equation: $4x - 50 + 50 = 110 + 50$ $4x = 160$ We add 50 to both sides to isolate the term with $x$ .
We're trying to get $x$ by itself!

STEP 9

Divide both sides by 4: $\frac{4x}{4} = \frac{160}{4}$ $x = 40$ We divide by 4 to get the value of a single $x$ .

STEP 10

Desiree answered 40 questions correctly.
The equation representing the situation is $3x - (50 - x) = 110$ .

Get Studdy

Studdy solves anything!

Start learning now

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

Studdy Solution

STEP 1

STEP 2

1. Set up the equation2. Simplify and solve

STEP 3

Let xxx be the number of questions Desiree answered correctly.Since there are 50 total questions and she answered all of them, the number of questions she answered incorrectly is 50−x50 - x50−x.

STEP 4

STEP 5

So, the equation representing the situation is: 3x−(50−x)=1103x - (50 - x) = 1103x−(50−x)=110

STEP 6

Distribute the negative sign in front of the parentheses: 3x−50+x=1103x - 50 + x = 1103x−50+x=110 We do this because subtracting a quantity is the same as adding its opposite.

STEP 7

Combine the xxx terms on the left side: 4x−50=1104x - 50 = 1104x−50=110 We're combining like terms to simplify the equation and make it easier to solve for xxx.

STEP 8

Add 50 to both sides of the equation: 4x−50+50=110+504x - 50 + 50 = 110 + 504x−50+50=110+50 4x=1604x = 1604x=160We add 50 to both sides to isolate the term with xxx.We're trying to get xxx by itself!

STEP 9

Divide both sides by 4: 4x4=1604\frac{4x}{4} = \frac{160}{4}44x​=4160​ x=40x = 40x=40We divide by 4 to get the value of a **single** xxx.

STEP 10

Desiree answered 40 questions correctly.The equation representing the situation is 3x−(50−x)=1103x - (50 - x) = 1103x−(50−x)=110.

Get Studdy

Studdy solves anything!

Start learning now

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

1. Set up the equation
2. Simplify and solve

Let $x$ be the number of questions Desiree answered correctly.
Since there are 50 total questions and she answered all of them, the number of questions she answered incorrectly is $50 - x$ .

So, the equation representing the situation is: $3x - (50 - x) = 110$

Distribute the negative sign in front of the parentheses: $3x - 50 + x = 110$ We do this because subtracting a quantity is the same as adding its opposite.

Combine the $x$ terms on the left side: $4x - 50 = 110$ We're combining like terms to simplify the equation and make it easier to solve for $x$ .

Add 50 to both sides of the equation: $4x - 50 + 50 = 110 + 50$ $4x = 160$ We add 50 to both sides to isolate the term with $x$ .
We're trying to get $x$ by itself!

Divide both sides by 4: $\frac{4x}{4} = \frac{160}{4}$ $x = 40$ We divide by 4 to get the value of a single $x$ .

Desiree answered 40 questions correctly.
The equation representing the situation is $3x - (50 - x) = 110$ .