BMST - Basic Math and Science Algebraic Equations and Inequalities Questions and Answers — Questions and Answers
Question 1: A school is organizing a field trip. The total cost is $1,200, which includes a fixed fee of $150 for the bus and a cost per student. If 75 students are attending, what is the cost per student?
- $14 (Correct answer)
- $16
- $18
- $12
Correct answer: $14
Let 'c' be the cost per student. The total cost can be represented by the equation 75c + 150 = 1200. To solve for c, first subtract 150 from both sides: 75c = 1050. Then, divide by 75: c = 1050 / 75. The result is c = 14.
Question 2: Which of the following is the correct solution set for the inequality 3(x - 4) > 5x + 2?
- x > 7
- x < 7
- x > -7
- x < -7 (Correct answer)
Correct answer: x < -7
First, distribute the 3 on the left side: 3x - 12 > 5x + 2. Next, get the x terms on one side by subtracting 5x from both sides: -2x - 12 > 2. Then, add 12 to both sides: -2x > 14. Finally, divide both sides by -2. Remember to reverse the inequality sign when multiplying or dividing by a negative number: x < -7.
Question 3: Solve the quadratic equation x² - 8x + 15 = 0.
- x = -3 and x = -5
- x = 3 and x = 5 (Correct answer)
- x = -3 and x = 5
- x = 3 and x = -5
Correct answer: x = 3 and x = 5
This quadratic equation can be solved by factoring. We need to find two numbers that multiply to 15 and add up to -8. These numbers are -3 and -5. So, the equation can be factored as (x - 3)(x - 5) = 0. According to the Zero-Product Property, either x - 3 = 0 or x - 5 = 0. Solving these gives x = 3 and x = 5.
Question 4: A rectangular garden has a perimeter of 120 feet. The length of the garden is 10 feet more than its width. What are the dimensions of the garden?
- Length = 40 ft, Width = 20 ft
- Length = 30 ft, Width = 30 ft
- Length = 35 ft, Width = 25 ft (Correct answer)
- Length = 25 ft, Width = 35 ft
Correct answer: Length = 35 ft, Width = 25 ft
Let 'w' be the width and 'l' be the length. We are given two pieces of information that can be turned into equations: 1) l = w + 10 and 2) 2l + 2w = 120. This is a system of linear equations. Substitute the first equation into the second: 2(w + 10) + 2w = 120. Distribute the 2: 2w + 20 + 2w = 120. Combine like terms: 4w + 20 = 120. Subtract 20 from both sides: 4w = 100. Divide by 4: w = 25. Now find the length: l = 25 + 10 = 35. So the dimensions are 35 ft by 25 ft.
Question 5: What is the solution for x in the equation (2/3)x - 4 = 6?
- x = 3
- x = 6
- x = 10
- x = 15 (Correct answer)
Correct answer: x = 15
To solve for x, first isolate the term with x by adding 4 to both sides of the equation: (2/3)x = 6 + 4, which simplifies to (2/3)x = 10. To solve for x, multiply both sides by the reciprocal of 2/3, which is 3/2. So, x = 10 * (3/2). This gives x = 30 / 2, which simplifies to x = 15.
Question 6: A movie theater charges $12 for an adult ticket and $8 for a child's ticket. On a particular day, 200 tickets were sold for a total revenue of $2,160. Which system of equations can be used to find the number of adult tickets (a) and child tickets (c) sold?
- a + c = 2160; 12a + 8c = 200
- a + c = 200; 12a + 8c = 2160 (Correct answer)
- 12a + 8c = 200; a - c = 2160
- a + c = 200; 20(a + c) = 2160
Correct answer: a + c = 200; 12a + 8c = 2160
The problem presents two distinct conditions that can be translated into two linear equations. The first equation represents the total number of tickets sold: the number of adult tickets (a) plus the number of child tickets (c) equals 200. This gives the equation a + c = 200. The second equation represents the total revenue: the revenue from adult tickets (12a) plus the revenue from child tickets (8c) equals $2,160. This gives the equation 12a + 8c = 2160.
BMST - Basic Math and Science Algebraic Equations and Inequalities Questions and Answers
A school is organizing a field trip.
The total cost is $1,200, which includes a fixed fee of $150 for the bus and a cost per student.
If 75 students are attending, what is the cost per student?