# 3.6 Solve applications with linear inequalities

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## Everyday math

Maximum Load on a Stage In 2014, a high school stage collapsed in Fullerton, California, when 250 students got on stage for the finale of a musical production. Two dozen students were injured. The stage could support a maximum of 12,750 pounds. If the average weight of a student is assumed to be 140 pounds, what is the maximum number of students who could safely be on the stage?

91 students

Maximum Weight on a Boat In 2004, a water taxi sank in Baltimore harbor and five people drowned. The water taxi had a maximum capacity of 3,500 pounds (25 people with average weight 140 pounds). The average weight of the 25 people on the water taxi when it sank was 168 pounds per person. What should the maximum number of people of this weight have been?

Wedding Budget Adele and Walter found the perfect venue for their wedding reception. The cost is \$9,850 for up to 100 guests, plus \$38 for each additional guest. How many guests can attend if Adele and Walter want the total cost to be no more than \$12,500?

169 guests

Shower Budget Penny is planning a baby shower for her daughter-in-law. The restaurant charges \$950 for up to 25 guests, plus \$31.95 for each additional guest. How many guests can attend if Penny wants the total cost to be no more than \$1,500?

## Writing exercises

Find your last month’s phone bill and the hourly salary you are paid at your job. (If you do not have a job, use the hourly salary you would realistically be paid if you had a job.) Calculate the number of hours of work it would take you to earn at least enough money to pay your phone bill by writing an appropriate inequality and then solving it.

Find out how many units you have left, after this term, to achieve your college goal and estimate the number of units you can take each term in college. Calculate the number of terms it will take you to achieve your college goal by writing an appropriate inequality and then solving it.

## Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

## 3.1 Using a Problem Solving Strategy

Approach Word Problems with a Positive Attitude

In the following exercises, reflect on your approach to word problems.

How has your attitude towards solving word problems changed as a result of working through this chapter? Explain.

Did the problem-solving strategy help you solve word problems in this chapter? Explain.

Use a Problem-Solving Strategy for Word Problems

In the following exercises, solve using the problem-solving strategy for word problems. Remember to write a complete sentence to answer each question.

Three-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert?

116

There are nine saxophone players in the band. The number of saxophone players is one less than twice the number of tuba players. Find the number of tuba players.

#### Questions & Answers

(a+b)(p+q+r)(b+c)(p+q+r)(c+a) (p+q+r)
4x-7y=8 2x-7y=1 what is the answer?
x=7/2 & y=6/7
Pbp
x=7/2 & y=6/7 use Elimination
Debra
true
bismark
factoriz e
usman
4x-7y=8 X=7/4y+2 and 2x-7y=1 x=7/2y+1/2
Peggie
Ok cool answer peggie
Frank
thanks
Ramil
copy and complete the table. x. 5. 8. 12. then 9x-5. to the 2nd power+4. then 2xto the second power +3x
What is c+4=8
2
Letha
4
Lolita
4
Rich
4
thinking
C+4=8 -4 -4 C =4
thinking
I need to study
Letha
4+4=8
William
During two years in college, a student earned \$9,500. The second year, she earned \$500 more than twice the amount she earned the first year.
9500=500+2x
Debra
9500-500=9000 9000÷2×=4500 X=4500
Debra
X + Y = 9500....... & Y = 500 + 2X so.... X + 500 + 2X = 9500, them X = 3000 & Y = 6500
Pbp
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles.
Reiko needs to mail her Christmas cards and packages and wants to keep her mailing costs to no more than \$500. The number of cards is at least 4 more than twice the number of packages. The cost of mailing a card (with pictures enclosed) is \$3 and for a package the cost is \$7.
hey
Juan
Sup
patrick
The sum of two numbers is 155. The difference is 23. Find the numbers
The sum of two numbers is 155. Their difference is 23. Find the numbers
Michelle
The difference between 89 and 66 is 23
Ciid
Joy is preparing 20 liters of a 25% saline solution. She only has 40% and 10% solution in her lab. How many liters of the 40% and how many liters of the 10% should she mix to make the 25% solution?
hello
bismark
I need a math tutor BAD
Stacie
Me too
Letha
me too
Xavier
ok
Bishal
teet
Bishal
Sue and Deb work together writing a book that takes them 90 days. If Sue worked alone, it would take her 120 days. How long would it take Deb to write the book alone?
Tell Deb to write the book alone and report back on how long it took her. Deb could get bored and stop, she could get sick next week and prolong the time, she could die next month. This question is impossible to answer.
vV
right*
tyler
is there a thumbs up mathematical symbol in algebra? 👍²= vV 90days x 120days =10800 120days - 90days = 30 10800days/30days= 360days? (ad) derall=1440 mins (90x ad )+(120 x ad )/(120 x ad ))-((90d x ad)= you go glen coco! I'll see my self out
Nick
Larry and Tom were standing next to each other in the backyard when Tom challenged Larry to guess how tall he was. Larry knew his own height is 6.5 feet and when they measured their shadows, Larry’s shadow was 8 feet and Tom’s was 7.75 feet long. What is Tom’s height?
6.25
Ciid
6.25
Big
?
Twila
Wayne is hanging a string of lights 57 feet long around the three sides of his patio, which is adjacent to his house. the length of his patio, the side along the house, is 5 feet longer than twice it's width. Find the length and width of the patio.
Ciid
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
SOH = Sine is Opposite over Hypotenuse. CAH= Cosine is Adjacent over Hypotenuse. TOA = Tangent is Opposite over Adjacent.
tyler
H=57 and O=285 figure out what the adjacent?
tyler
help
Twila
draw a diagram first
John
Amara currently sells televisions for company A at a salary of \$17,000 plus a \$100 commission for each television she sells. Company B offers her a position with a salary of \$29,000 plus a \$20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
what is the quantity and price of the televisions for both options?
karl
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000 17000+
Ciid
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000
Ciid
I'm mathematics teacher from highly recognized university.
here a question professor How many soldiers are there in a group of 27 sailors and soldiers if there are four fifths as many sailors as soldiers? can you write out the college you went to with the name of the school you teach at and let me know the answer I've got it to be honest with you
tyler
is anyone else having issues with the links not doing anything?
Yes
Val