Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Jayla is booking a band and a DJ for a dance, and wants to keep the cost of the entertainment under $1,100\$1,100. A band can play for part of the time at an hourly rate of $120\$120, and a DJ can play for the remaining time at an hourly rate of $80\$80.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of hours the band will play\newliney=y = the number of hours the DJ will play\newlineChoices:\newline(A) 80 + x + 120 + y < 1,100\newline(B) 120 + x + 80 + y < 1,100\newline(C) 120x + 80y < 1,100\newline(D) 80x + 120y < 1,100

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Write two-variable inequalities: word problemsright chevron icon

Full solution

Q. Jayla is booking a band and a DJ for a dance, and wants to keep the cost of the entertainment under $1,100\$1,100. A band can play for part of the time at an hourly rate of $120\$120, and a DJ can play for the remaining time at an hourly rate of $80\$80.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of hours the band will play\newliney=y = the number of hours the DJ will play\newlineChoices:\newline(A) 80+x+120+y<1,10080 + x + 120 + y < 1,100\newline(B) 120+x+80+y<1,100120 + x + 80 + y < 1,100\newline(C) 120x+80y<1,100120x + 80y < 1,100\newline(D) 80x+120y<1,10080x + 120y < 1,100
  1. Identify Cost Rates: Identify the cost per hour for the band and the DJ. The band costs $120\$120 per hour, and the DJ costs $80\$80 per hour. These rates are given in the problem statement.
  2. Define Variables: Define the variables for the number of hours the band and the DJ will play. According to the problem, xx represents the number of hours the band will play, and yy represents the number of hours the DJ will play.
  3. Band Total Cost: Write the expression for the total cost of the band. The total cost for the band is the band's hourly rate multiplied by the number of hours they play, which is 120x120x.
  4. DJ Total Cost: Write the expression for the total cost of the DJ. The total cost for the DJ is the DJ's hourly rate multiplied by the number of hours they play, which is 80y80y.
  5. Combine Total Costs: Combine the expressions for the total cost of the band and the DJ to get the total cost of the entertainment. The total cost is the sum of the cost for the band and the DJ, which is 120x+80y120x + 80y.
  6. Budget Constraint Inequality: Set up the inequality based on the budget constraint. Jayla wants to keep the total cost under $1,100\$1,100, so the inequality that represents this situation is 120x + 80y < 1,100.

More problems from Write two-variable inequalities: word problems

Question
Write the following inequality in slope-intercept form.\newline9x+y≥−179x+y \geq -17\newlineWrite your answer with yy first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form. \newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Does (2, 1)(2,\,1) make the inequality 2x+15y<202x + 15y < 20 true?\newlineChoices:\newlineyes\newlineno
Get tutor helpright-arrow

Posted 5 months ago

Question
Jack is fixing up his home and must spend less than $4,800\$4,800 to hire carpenters and painters. Carpenters charge $60\$60 per hour and painters charge $32\$32 per hour. \newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of hours of carpentry\newliney=y = the number of hours of painting\newlineChoices:\newline(A) 32x+60y<4,80032x + 60y < 4,800\newline(B) 60x+32y<4,80060x + 32y < 4,800 \newline(C) 32x−60y<4,80032x - 60y < 4,800 \newline(D) 60x−32y<4,80060x - 32y < 4,800
Get tutor helpright-arrow

Posted 5 months ago

Question
Is (2, 10)(2,\, 10) a solution to this system of inequalities?\newliney≥x+10y \geq x + 10\newliney≤9x+5y \leq 9x + 5\newlineChoices:\newline(A) yes\newline(B) no
Get tutor helpright-arrow

Posted 5 months ago

Question
Write the following inequality in slope-intercept form. \newline4x−2y≤84x - 2y \leq 8 \newline Write your answer with yy first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.
Get tutor helpright-arrow

Posted 9 months ago

Question
Write the following inequality in slope-intercept form. \newline−3x+5y>15-3x + 5y > 15 \newline Write your answer with yy first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.
Get tutor helpright-arrow

Posted 9 months ago

Question
Write the following inequality in slope-intercept form. \newline2x+3y<−62x + 3y < -6 \newline Write your answer with yy first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.
Get tutor helpright-arrow

Posted 9 months ago

Question
Write the following inequality in slope-intercept form. \newline−7x−y≥21-7x - y \geq 21 \newline Write your answer with yy first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.
Get tutor helpright-arrow

Posted 8 months ago

Question
Write the following inequality in slope-intercept form. \newline5x−4y>−205x - 4y > -20 \newline Write your answer with yy first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.
Get tutor helpright-arrow

Posted 9 months ago

Question
Miyoko's goal is to earn more than (950(950 this week. She earns )250)250 for every day she works as a cryptographer, and earns $180\$180 for every day she works as a geologist.\newlineWrite an inequality that represents the number of days Miyoko should work as a cryptographer CC and as a geologist GG to achieve her goal.
Get tutor helpright-arrow

Posted 10 months ago

View all (97)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant