Youssef is taking a trip on an airplane. He knows that to avoid extra fees his suitcase must weigh under 50 pounds. The suitcase with his clothes weighs 35 pounds. He has room, so he decides to pack some books for his trip, too. Each book weighs on average 1.2 pounds. How many books could he bring on the trip? He writes the inequality 1.2b+35<50 , where b equals the number of books, to help figure this out. Solve his inequality. Use the letter b as your variable and write your b term first..
To solve the inequality for the number of books Youssef can bring, we have:
1.2b + 35 < 50
First, we'll isolate the term with the variable (b) by subtracting 35 from both sides of the inequality:
1.2b + 35 - 35 < 50 - 35
1.2b < 15
Now, to solve for b, we'll divide both sides by 1.2:
1.2b / 1.2 < 15 / 1.2
b < 12.5
Since Youssef can't bring a fraction of a book on the trip, we round down to the nearest whole number. Therefore, Youssef can bring a maximum of 12 books on the trip without exceeding the 50-pound weight limit for his suitcase.
Lily is saving up to buy a cellphone. She needs to save at least $300 before she is able to buy the phone. Her grandfather gives her $40, and she earns $65 tutoring after school each week. Write an inequality for the number of weeks Lily will need to save to have at least $300, and describe the solutions.(2 points) x+ ≥, where x is the number of weeks Lily will need to save. Lily must save for at least weeks to have at least $300.
To write the inequality for the number of weeks Lily needs to save to have at least $300, let's denote the number of weeks she needs to save with the variable x. She earns $65 each week from tutoring, so the total amount she will earn from tutoring after x weeks will be 65x. She also has an initial amount of $40 from her grandfather.
The inequality that represents the situation will be:
65x + 40 ≥ 300
To find the number of weeks she needs to save, we must solve for x:
65x + 40 - 40 ≥ 300 - 40
65x ≥ 260
Now, divide both sides by 65 to solve for x:
65x / 65 ≥ 260 / 65
x ≥ 4
Lily will need to save for at least 4 weeks to have at least $300.
To solve the inequality 1.2b + 35 < 50, we want to isolate the variable b. Let's go through the steps:
1. Start with the given inequality: 1.2b + 35 < 50
2. Subtract 35 from both sides of the inequality to move the constant term to the right side: 1.2b < 50 - 35.
Simplifying, we have: 1.2b < 15.
3. To isolate the variable b, divide both sides of the inequality by 1.2: (1.2b)/1.2 < 15/1.2.
Simplifying, we have: b < 12.5.
Therefore, Youssef can bring up to 12 books on his trip to ensure that his suitcase weighs less than 50 pounds.