Practice Test 3 - Pre Algebra

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A machine produces $3\frac{3}{5}$ widgets in $\frac{4}{5}$ of a minute. What is the production rate in widgets per minute?
2. A recipe calls for ingredients in the ratio $2:3:5$ by weight. If the total weight of these three ingredients is $4.8$ kg, and one ingredient makes up $30\%$ of the mixture, what is the weight of the heaviest ingredient?
3. A rectangular field is 80 meters long and 60 meters wide. A diagonal path cuts across the field from one corner to the opposite corner. If a person walks along the perimeter from the same starting corner to the opposite corner, how many meters longer is the perimeter route compared to the diagonal path?
4. The equation $\frac{x + 5}{3} = 8$ has the same solution as which of the following equations?
5. A water tank loses $\frac{1}{6}$ of its water each day due to evaporation. If the tank starts with $\frac{4}{5}$ of its capacity filled, what fraction of the tank's total capacity remains after 2 days?
6. A student simplified $5a^2b - 3ab^2 + 2a^2b + 4ab^2 - ab^2$ and got $7a^2b + 0ab^2$. The student then wrote the final answer as $7a^2b$. What error, if any, did the student make?
7. A water tank is being filled at a rate of 15 gallons per minute and drained at a rate of 8 gallons per minute simultaneously. The tank starts with 120 gallons and must maintain at least 50 gallons at all times for safety reasons. Which inequality represents the time constraint $t$ (in minutes) for how long this process can continue?
8. Point $A$ is located at $-12$ on a number line. Point $B$ is the same distance from zero as point $A$, but in the opposite direction. Point $C$ is located so that the distance from $C$ to zero equals the distance from $A$ to $B$. How many possible locations are there for point $C$?
9. Two competing cell phone plans charge data overage fees of 0.025 dollars per MB and 2.8% of a dollar per MB, respectively. What is the difference between these rates expressed as a percentage of a dollar?
10. A store marks up items by $37.5\%$ above cost. If an item costs the store $24, what fraction of the selling price represents the store's profit?
11. The formula for the volume of a triangular prism is $V = \frac{1}{2}bhl$, where $b$ is the base of the triangle, $h$ is the height of the triangle, and $l$ is the length of the prism. A triangular prism has a volume of $180$ cubic centimeters, a triangular base with height $6$ cm, and the prism length is $5$ cm. What is the length of the triangle's base?
12. The circumference of a circular pond is $24\pi$ feet. A walkway extends 3 feet beyond the pond's edge in all directions. What is the area of the walkway only?
13. A bakery uses a mixture that is $60\%$ flour and $40\%$ other ingredients by weight. If they want to create a new mixture that is $75\%$ flour by adding pure flour, how much pure flour must they add to $20$ pounds of the original mixture?
14. A cell phone plan costs $25 per month plus $0.10 per text message. If $C$ represents the total monthly cost and $t$ represents the number of text messages, which statement correctly interprets both the slope and y-intercept of the equation $C = 0.10t + 25$?
15. Marcus has $45.80 and spends $12.95 on lunch, then $8.75 on a book. He finds $2.40 on the ground. Later, he buys a snack for $3.85. How much money does he have now?
16. A circular running track has an inner radius of 40 meters and an outer radius of 45 meters. What is the area of the track itself (the region between the two circles)?
17. If $a = 2^3$ and $b = 3^2$, what is the value of $a^2 + b \times 4 - 2a$?
18. A rectangular garden must have a perimeter of exactly 48 feet, and its length must be at least 4 feet longer than its width. If $w$ represents the width in feet, which system correctly represents both constraints?
19. A clothing store has a '30% off everything' sale. During the sale, an item that originally cost $150 is marked down. The next week, the store raises all sale prices by 25%. What is the final price of this item?
20. Which statement is always true about any real number $x$ and its opposite?

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