ATDH - Admission Test for Dental Hygiene Quantitative Reasoning: Algebra Questions and Answers — Questions and Answers
Question 1: A dental clinic budgets its monthly expenses based on the number of patients seen. The clinic's fixed costs are $15,000 per month. The variable cost per patient is $25. If the total monthly expenses were $27,500, which equation correctly represents the situation and how many patients (p) were seen that month?
- 15000p + 25 = 27500; This is not the correct model.
- 15000 + 25p = 27500; 500 patients (Correct answer)
- 15000 + 27500 = 25p; 1700 patients
- 25p - 15000 = 27500; 1700 patients
Correct answer: 15000 + 25p = 27500; 500 patients
The total monthly expense is the sum of the fixed costs and the total variable costs. The total variable cost is the cost per patient ($25) times the number of patients (p). Therefore, the equation is 15000 + 25p = 27500. To solve for p, subtract 15000 from both sides: 25p = 12500. Then, divide by 25: p = 500.
Question 2: A dental hygienist mixes a 2% fluoride solution with a 10% fluoride solution to create 80 ml of a 5% fluoride solution. How many milliliters of the 10% solution are needed?
- 50 ml
- 20 ml
- 30 ml (Correct answer)
- 60 ml
Correct answer: 30 ml
Let x be the amount of the 2% solution and y be the amount of the 10% solution. The two equations are x + y = 80 (total volume) and 0.02x + 0.10y = 0.05 * 80 (total fluoride amount). From the first equation, x = 80 - y. Substitute this into the second equation: 0.02(80 - y) + 0.10y = 4. This simplifies to 1.6 - 0.02y + 0.10y = 4. Then, 0.08y = 2.4. Solving for y gives y = 30 ml.
Question 3: Which of the following inequalities represents the range of values for 'x' if |3x - 6| < 9?
- x > 5 or x < -1
- x < 5
- x > -1
- -1 < x < 5 (Correct answer)
Correct answer: -1 < x < 5
The absolute value inequality |3x - 6| < 9 can be rewritten as -9 < 3x - 6 < 9. To solve for x, first add 6 to all three parts of the inequality: -9 + 6 < 3x < 9 + 6, which simplifies to -3 < 3x < 15. Finally, divide all three parts by 3: -1 < x < 5.
Question 4: The number of bacteria in a culture triples every 4 hours. If the initial number of bacteria is B, what is the expression that represents the number of bacteria after 24 hours?
- B * 3^6 (Correct answer)
- B * 3^4
- B * 3^24
- B * (3*6)
Correct answer: B * 3^6
The bacteria triples every 4 hours. In a 24-hour period, this tripling event occurs 24 / 4 = 6 times. Therefore, the initial number of bacteria, B, must be multiplied by 3 six times. This is represented by the exponential expression B * 3^6.
Question 5: A dental supply company sells two types of gloves, latex and nitrile. The ratio of the price of a box of latex gloves to a box of nitrile gloves is 3:5. If a box of nitrile gloves costs $12.50, what is the cost of a box of latex gloves?
- $20.83
- $4.17
- $7.50 (Correct answer)
- $9.50
Correct answer: $7.50
Let the price of latex gloves be 3x and the price of nitrile gloves be 5x. We are given that the price of nitrile gloves is $12.50. So, 5x = $12.50. Solving for x, we get x = $12.50 / 5 = $2.50. The cost of the latex gloves is 3x, so 3 * $2.50 = $7.50.
Question 6: Solve the following equation for x: (2x + 5) / 3 = 3x - 5
- x = -2
- x = 20/7 (Correct answer)
- x = 10/7
- x = 20/11
Correct answer: x = 20/7
To solve the equation, first multiply both sides by 3 to eliminate the denominator: 2x + 5 = 3(3x - 5). Distribute the 3 on the right side: 2x + 5 = 9x - 15. Next, get the x terms on one side by subtracting 2x from both sides: 5 = 7x - 15. Then, add 15 to both sides: 20 = 7x. Finally, divide by 7 to solve for x: x = 20/7.
ATDH - Admission Test for Dental Hygiene Quantitative Reasoning: Algebra Questions and Answers
A dental clinic budgets its monthly expenses based on the number of patients seen.
The clinic's fixed costs are $15,000 per month.
The variable cost per patient is $25.
If the total monthly expenses were $27,500, which equation correctly represents the situation and how many patients (p) were seen that month?