Fifteen less than four times a number is more than 49. What are all the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter x as your variable and write your x term first.
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.
Youssef has written the inequality as:
1.2b + 35 < 50
This expresses that the weight of the books (1.2 pounds times the number of books b) plus the weight of the suitcase with clothes (35 pounds) must be less than 50 pounds to avoid extra fees.
To solve the inequality for b (the number of books), we need to get b by itself on one side. Here's how you can solve the inequality:
1. Subtract 35 from both sides of the inequality to isolate the term involving b:
1.2b + 35 - 35 < 50 - 35
1.2b < 15
2. Now, we need to divide both sides by 1.2 to find the value of b:
1.2b / 1.2 < 15 / 1.2
b < 15 / 1.2
b < 12.5
Since Youssef cannot pack a fraction of a book, we need to consider only whole numbers of books. Therefore, Youssef could pack up to 12 books, because packing 13 books would result in a total weight of:
1.2 * 13 + 35 = 15.6 + 35 = 50.6 pounds
which exceeds the 50-pound limit.
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. Note: You will find the option to add a > , < , ≥ , or ≤ symbol in the Comparison (<) keyboard.
Youssef's inequality is:
1.2b + 35 < 50
To find out how many books he can bring on the trip, let's solve for b:
First, subtract 35 from both sides of the inequality to isolate the term involving b:
1.2b + 35 - 35 < 50 - 35
This simplifies to:
1.2b < 15
Now, divide both sides by 1.2 to solve for b:
1.2b / 1.2 < 15 / 1.2
b < 15 / 1.2
b < 12.5
Since Youssef cannot pack half of a book, we must round this number down to the nearest whole number. Therefore, Youssef can pack up to 12 books, as 13 books would put him over the 50-pound limit.
So, the solution for b is:
b ≤ 12
This means Youssef can bring 12 or fewer books on his trip to ensure the suitcase remains under the 50-pound weight limit.
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 an inequality for the number of weeks, Lily will need to save to have at least $300, we'll first represent the total amount of money Lily saves over x weeks as $65x, where x is the number of weeks she tutors. She also has $40 from her grandfather.
The inequality will describe the total money saved being at least $300:
65x + 40 ≥ 300
Now, to solve for x, we'll isolate the x term:
1. Subtract 40 from both sides of the inequality:
65x + 40 - 40 ≥ 300 - 40
65x ≥ 260
2. Now, divide both sides by 65 to solve for x:
65x / 65 ≥ 260 / 65
x ≥ 4
This means that Lily must save for at least 4 weeks to have at least $300.
So, the solutions to the inequality 65x + 40 ≥ 300 are all the values of x that are greater than or equal to 4. Lily must save for at least 4 weeks to have at least $300.
To write an inequality that represents the statement "fifteen less than four times a number is more than 49", we first need to define the variable x as the number.
Translate the statement step by step into an algebraic inequality:
- "four times a number" is represented as 4x
- "fifteen less than four times a number" is represented as 4x - 15
- "is more than 49" translates to > 49
Putting it all together, we get:
4x - 15 > 49
Now, to express all possible values of the number (x), we need to solve the inequality:
4x - 15 > 49
Add 15 to both sides to get:
4x > 49 + 15
4x > 64
Now divide both sides by 4 to solve for x:
x > 64 / 4
x > 16
This means that all possible values for the number x must be greater than 16. So any number greater than 16 satisfies the inequality.