Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In order to win a quiz contest, Olga must score more than 400 points. She earns 12 points for each right answer, and loses 4 points for each wrong answer.
Write an inequality that represents the number of right answers
(R) and wrong answers
(W) Olga can give to win the contest.

In order to win a quiz contest, Olga must score more than $400$ points. She earns $12$ points for each right answer, and loses $4$ points for each wrong answer. $\newline$ Write an inequality that represents the number of right answers $(R)$ and wrong answers $(W)$ Olga can give to win the contest.

View step-by-step help

View step-by-step help

Modeling with linear inequalities

Full solution

Q. In order to win a quiz contest, Olga must score more than

400

points. She earns

12

points for each right answer, and loses

4

points for each wrong answer.

\newline

Write an inequality that represents the number of right answers

(R)

and wrong answers

(W)

Olga can give to win the contest.

Identify Points: Identify the points Olga earns for each right answer and loses for each wrong answer. $\newline$ Olga earns $12$ points for each right answer and loses $4$ points for each wrong answer.
Set up Inequality: Set up an inequality to represent the total points Olga must score to win the contest. $\newline$ Olga must score more than $400$ points to win the contest.
Translate to Algebraic Inequality: Translate the given information into an algebraic inequality. $\newline$ The total points Olga scores is the sum of the points from right answers minus the points lost from wrong answers. This total must be greater than $400$ . $\newline$ So, the inequality is $12R - 4W > 400$ .
Check Inequality: Check the inequality to ensure it represents the situation correctly. $\newline$ For each right answer, Olga's score increases by $12$ points, and for each wrong answer, her score decreases by $4$ points. The inequality $12R - 4W > 400$ correctly represents the condition that Olga's score must be more than $400$ points to win.

More problems from Modeling with linear inequalities

Question

Write the following inequality in slope-intercept form.

\newline

9x+y \geq -17

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

\newline

Posted 3 months ago

Question

(2,\,1)

make the inequality

2x + 15y < 20

\newline

\newline

\newline

Posted 3 months ago

Question

Jack is fixing up his home and must spend less than

\$4,800

to hire carpenters and painters. Carpenters charge

\$60

per hour and painters charge

\$32

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of hours of carpentry

\newline

y =

the number of hours of painting

\newline

\newline

32x + 60y < 4,800

\newline

60x + 32y < 4,800

\newline

32x - 60y < 4,800

\newline

60x - 32y < 4,800

Posted 3 months ago

Question

(2,\, 10)

a solution to this system of inequalities?

\newline

y \geq x + 10

\newline

y \leq 9x + 5

\newline

\newline

\newline

Posted 3 months ago

Question

Write the following inequality in slope-intercept form.

\newline

4x - 2y \leq 8

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

Posted 4 months ago

Question

Write the following inequality in slope-intercept form.

\newline

-3x + 5y > 15

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

Posted 4 months ago

Question

Write the following inequality in slope-intercept form.

\newline

2x + 3y < -6

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

Posted 4 months ago

Question

Write the following inequality in slope-intercept form.

\newline

-7x - y \geq 21

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

Posted 2 months ago

Question

Write the following inequality in slope-intercept form.

\newline

5x - 4y > -20

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

Posted 4 months ago

Question

Miyoko's goal is to earn more than

(950

this week. She earns

)250

for every day she works as a cryptographer, and earns

\$180

for every day she works as a geologist.

\newline

Write an inequality that represents the number of days Miyoko should work as a cryptographer

C

and as a geologist

G

to achieve her goal.

Posted 4 months ago