BMST - Basic Math and Science Algebraic Equations and Inequalities 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?

Accepted Answer

$14

Answer

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?

Accepted Answer

x < -7

Answer

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.

Accepted Answer

x = 3 and x = 5

Answer

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?

Accepted Answer

Length = 35 ft, Width = 25 ft

Answer

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?

Accepted Answer

x = 15

Answer

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.

BMST - Basic Math and Science Test Practice Test

BMST - Basic Math and Science Test Practice Test

BMST - Basic Math and Science Algebraic Equations and Inequalities Questions and Answers