A school is organizing a weekend trip to a nature preserve. For each student, there is a $60 charge, which covers food and lodging. There is also a $40 charge per student for the bus. The school must also pay a $30 cleaning fee for the bus. If the total cost of the weekend is $4,030, how many students will be going on the trip?
31 students
40 students
41 students
66 students
Let's start by setting up an equation to represent the total cost of the trip:
Total Cost = (Cost per Student x Number of Students) + Bus Cost + Bus Cleaning Fee
We know that the cost per student is $60, so we can substitute that in:
Total Cost = ($60 x Number of Students) + Bus Cost + Bus Cleaning Fee
We also know that the bus cost is $40 per student, and the cleaning fee is a flat $30, so we can substitute those in as well:
Total Cost = ($60 x Number of Students) + ($40 x Number of Students) + $30
Simplifying this, we get:
Total Cost = $100 x Number of Students + $30
We're given that the total cost of the weekend is $4,030, so we can substitute that in and solve for the number of students:
$4,030 = $100 x Number of Students + $30
$4,000 = $100 x Number of Students
Number of Students = 40
Therefore, there are 40 students going on the trip. Answer: \boxed{40}.
Arianne is taking a geometry course and is working with the area of triangles. She knows the area and the height but needs to find the base. Rearrange the following equation for b, where A is the area, b is the base, and h is the height of the triangle.
A = one half b times h
b = 2A − h
b equals two times A over h
b = 2A + h
b = 2Ah
We start by using algebra to isolate b on one side of the equation:
A = (1/2)bh
Multiply both sides by 2 to get rid of the fraction:
2A = bh
Divide both sides by h to isolate b:
b = 2A/h
Therefore, the equation rearranged for b is:
b = 2A/h
Answer: \boxed{b = 2A/h}.
To complete a home repair, a carpenter is renting a tool from the local hardware store. The expression 15x + 50 represents the total charges, which includes a fixed rental fee and an hourly fee, where x is the hours of the rental. What does the constant term of the expression represent?
The total hourly rental fee paid for the tool
The fixed rental fee for the tool
The fee charged per hour for the tool
The total charge for the tool rental
The constant term in the expression 15x + 50 is the number 50. This represents the fixed rental fee for the tool.
The fixed rental fee is a flat fee that the carpenter pays regardless of how many hours they rent the tool for. In this case, the fixed rental fee is $50.
The expression also includes an hourly fee of $15, which is multiplied by the number of hours rented (x).
So, the full expression 15x + 50 represents the total charges for the tool rental, which includes both the fixed rental fee and the hourly fee.
Therefore, the constant term represents the fixed rental fee for the tool.
Answer: \boxed{The fixed rental fee for the tool}.
Determine the solutions of the equation:
the absolute value quantity four thirds times x plus 2 end quantity minus 6 equals 0
x = 3 and x = 6
x = −3 and x = 6
x = −3 and x = 3
x = −6 and x = 3
We start by isolating the absolute value term by adding 6 to both sides:
| (4/3)x + 2 | = 6
Next, we can split this equation into two separate cases, one where the expression inside the absolute value is positive, and one where it's negative:
Case 1: (4/3)x + 2 > 0 (which means (4/3)x > -2, and x > -3/2)
| (4/3)x + 2 | = (4/3)x + 2
(4/3)x + 2 = 6
(4/3)x = 4
x = 3
Case 2: (4/3)x + 2 < 0 (which means (4/3)x < -2, and x < -3/2)
| (4/3)x + 2 | = - (4/3)x - 2
-(4/3)x - 2 = 6
-(4/3)x = 8
x = -6
So the solutions to the equation are x = 3 and x = -6.
Answer: \boxed{x = 3 \text{ and } x = -6}.
Rich and Aylen are saving money to buy baseball tickets. Rich has $5 more than 3 times the amount of money Aylen has. Together, they have $101. Write an equation to determine how much money Rich and Aylen have together.
3x + 5 = 101
x + 3x − 5 = 101
x + 3x + 5 = 101
x − 3x − 5 = 101
Let's use a variable to represent the amount of money Aylen has, and use the given information to set up an equation to represent the total amount of money they have together.
Let x be the amount of money Aylen has.
Then, we're given that Rich has $5 more than 3 times the amount Aylen has:
Rich's amount = 3x + 5
Together, they have $101:
Total amount = x + 3x + 5 = 4x + 5
We can set up an equation using this expression for the total amount:
4x + 5 = 101
Subtracting 5 from both sides, we get:
4x = 96
Dividing both sides by 4, we get:
x = 24
So, Aylen has $24.
To find how much money they have together, we can substitute x = 24 into the expression for the total amount:
Total amount = 4x + 5 = 4(24) + 5 = 96 + 5 = 101
Therefore, Rich and Aylen have $101 together.
Answer: \boxed{x + 3x + 5 = 101}.
Chris saved x dollars and spent half of his savings buying video games. After earning an additional $20 cutting grass, he had $60. If the equation one half times x plus 20 equals 60 represents the scenario, how much did he start with in his savings?
$20
$40
$80
$160
We are given the equation:
(1/2)x + 20 = 60
To solve for x, we can start by subtracting 20 from both sides:
(1/2)x = 40
Then, we can multiply both sides by 2 to eliminate the fraction:
x = 80
Therefore, Chris started with $80 in his savings.
Answer: \boxed{\$80}.
Abbey wants to use her savings of $1,325 to learn yoga. The total charges to learn yoga include a fixed registration fee of $35 and a monthly fee of $50. Choose the inequality that would be used to solve for the maximum number of months for which Abbey can learn yoga with her savings.
35x + 50 ≤ 1,325
35 + 50x ≥ 1,325
35 + 50x ≤ 1,325
35x + 50 ≥ 1,325
The total cost of Abbey's yoga program is a fixed registration fee of $35 plus a monthly fee of $50 per month. If she wants to ensure that she has enough savings to cover the total cost of learning yoga for a certain number of months, we can use an inequality to express this as:
Total cost ≤ Savings
If we let x be the number of months that Abbey can learn yoga with her savings, the total cost of learning yoga for x months would be:
Total cost = $35 + $50x
So, we can write the inequality as:
$35 + $50x ≤ $1,325
Multiplying both sides by 100 cents, we get:
3500 + 5000x ≤ 132500
Simplifying this, we get:
5000x ≤ 129000
Dividing both sides by 5000, we get:
x ≤ 25.8
Therefore, the maximum number of months for which Abbey can learn yoga with her savings is 25 months (since she can't learn yoga for a partial month).
The inequality that represents this is:
35 + 50x ≤ 1325
Answer: \boxed{35 + 50x \leq 1,325}.