inequality

A car salesman earns $800 per month plus a 10% commission on the value of sales he makes for the month. If he is aiming to earn a minimum of $3200 a month, what is the possible value of sales that will enable this? to start, we have: Let the salesman's monthly sales be s. With a 10% discount...

Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today? Let m be the number of minutes. The phrase at least means an inequality, also known as greater than or equal to. So we have: m >= 11*6 m >= 66 You can read this as...

A bank charges a service fee of $7.50 per month for a checking account. A bank account has $85.00. If no money is deposited or withdrawn except the service charge, how many months until the account balance is negative? Let m be the number of months. Our balance is denoted by B(m): B(m) = 85 -...

Beverly has $50 to spend at an amusement park. She plans to spend $10 for food, and $15 for admission to the park. Each ride costs $1.50 to ride. Write an inequality to represent the possible number of rides she can ride? First, we subtract the food and admission cost from Beverly's starting...

a company has revenue given by R(x)=500x dollars and total cost given by C(x)=48,000 + 100x dollars, where x is the number of units produced and sold. How many units will give a profit Profit P(x) is given by: R(x) - C(x) So we have: P(x) = 500x - (100x + 48,000) P(x) = 500x - 100x - 48,000...

Determine whether the statement is true or false. If 0 < a < b, then Ln a < Ln b We have a logarithmic property that states: ln(a) - ln(b) = ln (a / b) We're given a < b, so (a / b) < 1 Therefore: ln (a / b) < 0 And since ln(a) - ln(b) = ln (a / b) Then Ln(a) - Ln(b) < 0 Add Ln(b) to...

Suppose we need 4 eggs to make a cake. If there are 24 eggs, write an inequality representing the possible number of cakes we can make. Set up a proportion of eggs to cakes where c is the number of cakes per 24 eggs: 4/1 <= 24/c Typing this proportion inequality into our search engine, we get...

You and five friends are planning a trip. You want to keep the cost less than $85 per person. You and five friends means you have: 5 + 1 = 6 people. If you want a cost per person less than 85, then we have a cost c such that: c/6 < 85

You have $20 to spend on taxi fare. The ride costs $5 plus $2.50 per kilometer. Write the inequality. Let k be the number of kilometers. We want our total to be $20 or less. We have the following inequality: 2.50k + 5 <= 20

Choose the best inequality for this scenario. Casey bought a sandwich and a drink for $3.75. If she has $6.00 to spend, what is the most she can spend on dessert? Let dessert spend be d. We have: d <= $6.00 - $3.75 d <= $2.25

a total of one and x is less than 5 A total of one and x means we add x to 1: 1 + x We set up an inequality, where 1 + x is less than (<) 5 1 + x < 5

Charmaine’s fish tank has 16 liters of water in it. she plans to add 6 liters per minute until the tank has at least 58 liters. What are the possible numbers of minutes Charmaine could add water? This is an algebraic inequality. The phrase at least means greater than or equal to. So we have: 6m...

You have $6.50 to make copies. It cost $0.45. Write and solve an equality that represents the number of copies Hoow many exact copies can you make? Let the number of copies be c. We have: 0.45c = 6.50 Type this equation into our search engine and we get: c = 14.444 We round down and say we...

Craig went bowling with $25 to spend. He rented shoes for $5.25 and paid $4.00 for each game. What was the greatest number of games Craig could have played? Set up the cost function C(g) where g is the number of games Craig plays: C(g) = Game fee * number of games (g) + shoe rental fee C(g) =...

You have to pay 29 a month until you reach 850 how many months will that take. Let m be the number of months. We set up the inequality: 29m > = 850 <-- We want to know when we meet or exceed 850, so we use greater than or equal to Type this inequality into our search engine, and we get: m >=...

Jody is buying a scrapbook and sheets of designer paper. She has $40 and needs at least $18.25 to buy the scrapbook. Each sheet of paper costs $0.34. How many sheets of paper can she buy? Set up a cost equation for the number of pieces of paper (p): 0.34p + 18.25 <= 40 <-- we have an...

A local sports centre charges $8 per visit. For an annual membership fee of$45, the cost per visit is only $5.50. What is the least number of visits needed in a year in order for the membership to be a better deal? Set up the cost for the visitors plan C(v) where v is the number of visits: C(v)...

Sarah makes $9 per hour working at a daycare center and $12 per hour working at a restaurant. Next week, Sarah is scheduled to work 8 hours at the daycare center. Which of the following inequalities represents the number of hours (h) that Sandra needs to work at the restaurant next week to earn...

d squared is greater than or equal to 17 d squared means we raise the variable d to the power of 2: d^2 The phrase greater than or equal to means an inequality. So we set this up using the >= in relation to 17: d^2 >= 17

Julie has $300 to plan a dance. There is a one-time fee of $75 to reserve a room. It also costs $1.50 per person for food and drinks. What is the maximum number of people that can come to the dance? Let each person be p. We have the following relationship for cost: 1.50p + 75 <=300 We use the...