ATDH - Admission Test for Dental Hygiene Quantitative Reasoning: Algebra 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?

Accepted Answer

15000 + 25p = 27500; 500 patients

Answer

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?

Accepted Answer

30 ml

Answer

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?

Accepted Answer

-1 < x < 5

Answer

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?

Accepted Answer

B * 3^6

Answer

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?

Accepted Answer

$7.50

Answer

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.

ATDH - Admission Test for Dental Hygiene Practice Test

ATDH - Admission Test for Dental Hygiene Practice Test

ATDH - Admission Test for Dental Hygiene Quantitative Reasoning: Algebra Questions and Answers