4.12 Problem solving with inequalities
Write and solve an inequality for the following statements:
5 groups of p, added to 5, is less than 25.
The sum of 2 groups of x and 1 is at least 7.
8 times x minus 5 is less than 35.
5 subtracted from 4 groups of n is greater than 11.
5 more than one half of p is less than 103.
24 less than one quarter of z is less than or equal to 2.
3 groups of y divided by 4 is less than or equal 6.
The sum of m and 10 divided by -2 is greater than 12.
Consider the following statement: "Two less than 4 groups of p is no more than 18".
Write and solve the inequality.
Find the greatest value of p that satisfies this condition.
Sophia has a budget for school stationery of \$32, but has already spent \$15.25 on books and folders.
Write an inequality that shows how much Sophia can spend on other stationery, where p represent the amount she can spend, and solve for p.
Xavier is not very good at saving his pocket money. Looking at the receipts for all of his purchases from the last week, Xavier can see that he has spent \$33.40. He really wants to go to the movies with his friends on the weekend but needs to have \$32.00.
Write an inequality that shows how much money Xavier must have had in his account at the beginning of the week to afford his weekend plans, where A represents the amount of money in Xavier's bank account at the beginning of the week and solve for A.
Sarah is gathering signatures on a petition to save the orangutans. She needs at least 9000 signatures to get mentioned on the "Save the Orangutans" website. If she gets 3 times the number of signatures that she has right now whe will achieve her goal.
If n represents the number of signatures Sarah has now, write an inequality and solve for n.
At a sport clubhouse, the coach wants to rope off a rectangular area that is adjacent to the building. He uses the length of the building as one side of the area, which measures 26 \text{ yd}. He has at most 42 \text{ yd} of rope available to use.
If the width of the roped area is W, write an inequality and solve for the range of possible widths.
Oprah charges \$34.50 to style hair, as well as \$4 per foil. Pauline would like a style and foil, but has no more than \$58.50 to spend.
If N represents the number of foils Pauline could get, write an inequality and solve for N.
To get a grade of C, John must obtain a total score of at least 300 over his four exams. So far, he has taken the first three exams and gotten scores of 63, 73, and 98.
If x represents what he must score on the last exam to get a grade C or better, write an inequality and solve for x.
Skye was given \$72 for a birthday present. This present, along with earnings from a Saturday job, is being set aside for a mountain bike. The job pays \$5.00 per hour and the bike costs \$379.
Write and solve an inequality to find the minimum number of hours that Skye needs to work to be able to buy the mountain bike, where h represents the number of hours worked. Round your answer to one decimal place.
If Skye can only work her job for a whole number of hours, find the minimum number of hours she must work to afford her bike.
Sean wants to save up enough money so that he can buy a new sports equipment set, which costs \$50.00. Sean has \$15.50 he saved from his birthday. In order to make more money, he plans to wash neighbors’ windows for \$2 per window.
Let w be the number of windows that Sean washes. Write and solve an inequality to find the minimum number of windows he needs to wash in order to afford the equipment set.
Find the minimum whole number of windows that Sean must wash to be able to afford the set.
James wants to order some books from an online bookstore. Each book costs \$13.30 and shipping for the entire order is a flat rate of \$29.05. James can spend no more than \$74.00.
If B represents the possible number of books that James can buy, write an inequality and solve for B. Round your answer to one decimal place.
Find the maximum number of books that James can afford to buy.
Jimmy spends \$120 to produce some cantaloupes. He is able to sell each one for \$9.
If n represents the number of cantaloupes he must sell to make a profit, write an inequality and solve for n.
Find the least number of cantaloupes that Jimmy must sell to make a profit.
Lachlan is planning on going on vacation. He has saved \$2118.40 and spends \$488.30 on his airplane ticket.
Let x represent the amount of money Lachlan spends on the rest of his vacation. Write an inequality to represent the situation, and then solve for x.
Find the greatest amount that Lachlan could spend on the rest of his holiday.