第3章数学モデル

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?

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?

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?

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.

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.

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?

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.

The sum of a number and three is forty-one. Find the number.

Twice the difference of a number and ten is fifty-four. Find the number.

One number is nine less than another. Their sum is negative twenty-seven. Find the numbers.

One number is eleven more than another. If their sum is increased by seventeen, the result is 90. Find the numbers.

One number is two more than four times another. Their sum is $\mathrm{-13}.$ Find the numbers.

The sum of two consecutive integers is $\mathrm{-135}.$ Find the numbers.

Find three consecutive integers whose sum is $\mathrm{-141}.$

Find three consecutive even integers whose sum is 234.

Find three consecutive odd integers whose sum is 51.

Koji has $5,502 in his savings account. This is $30 less than six times the amount in his checking account. How much money does Koji have in his checking account?