Pre-Algebra

A community center hosted 5 different skill workshops on a Saturday. The table below shows the number of participants in each workshop and the mean satisfaction rating (on a scale from 1 to 10) reported by the participants in that workshop.

What is the overall weighted mean satisfaction rating for all $50$ participants combined across all five workshops?

A fair game spinner is divided into $8$ equal sectors numbered $1$ through $8$. If Maya spins the spinner once, what is the probability that the spinner lands on a number strictly greater than $5$?

A freight shipping company calculates the total fuel consumption, $C$ in gallons, for a cargo vessel using the equation $C = 45h$, where $h$ represents the number of hours the vessel operates at cruising speed. If the vessel consumed a total of $3,150$ gallons of fuel on a recent journey, for how many hours did the vessel operate at cruising speed?

A high school robotics team recorded their scores across 5 qualification matches: $90, 78, 86, 82,$ and $84$. In their 6th qualification match, the team earned a score of $x$, which increased their overall 6-match mean score by $3$ points compared to their 5-match mean score. What is the positive difference between the median and the mean of all 6 match scores?

A juice bar allows customers to create a custom smoothie by selecting exactly $1$ fruit base out of $4$ available options and $1$ liquid base out of $3$ available options. How many different custom smoothie combinations of $1$ fruit base and $1$ liquid base are possible?

An artisan pottery workshop uses a total of $c$ kilograms of clay to make ceramic vases. If each vase requires $4$ kilograms of clay and the workshop produced $18$ vases in total, which of the following equations models this scenario, and what is the total amount of clay $c$ used?

A commercial printing press uses large rolls of paper for magazine production. During a morning shift, a technician uses $\frac{4}{9}$ of the total mass, $m$ (in kilograms), of a full paper roll. If the mass of paper used during the shift is $36$ kilograms, what is the total mass $m$, in kilograms, of the full paper roll?

Four real estate agents reported the proportion of their home listings that sold above asking price last month as follows: Agent W reported $\frac{31}{50}$, Agent X reported $\frac{5}{8}$, Agent Y reported $63\%$, and Agent Z reported $0.64$. Place the four agents in order from the smallest proportion of listings sold above asking price to the largest proportion.

A custom bicycle workshop builds specialized cargo bikes. The total frame assembly weight, $W$ pounds, is determined by adding a fixed base frame weight of $f$ pounds to the weight of $n$ reinforced structural struts, where each strut weighs 2.4 pounds. For a cargo bike configured with 5 structural struts, the total frame assembly weight is 26.0 pounds. Which of the following one-step linear equations can be solved to find $f$, the weight in pounds of the fixed base frame?

An automated manufacturing line produces component X and component Y in a ratio of $4:7$. During a single production run, a total of $1,760$ components were produced. How many more component Y than component X were produced during this run?

A community garden allocates its total area among three crops: vegetables, herbs, and flowers. Exactly $\frac{3}{8}$ of the total area is dedicated to vegetables, and $40\%$ of the remaining area is planted with herbs. If the remaining flower section covers $270$ square feet, what is the total area, in square feet, of the community garden?

A bookstore recorded the number of books purchased by a sample of $25$ customers. The frequency table below summarizes the purchases made by $20$ of these customers:

The remaining $5$ customers each purchased the exact same number of books, $n$. If the mean number of books purchased by all $25$ customers is $2.8$, what is the median number of books purchased by the entire group of $25$ customers?

A university professor teaches two sections of Introductory Statistics. Section 1 contains $30$ students and had a mean score of $82$ on the midterm exam. Section 2 contains $20$ students and had a mean score of $92$ on the same exam. What is the overall mean midterm exam score for all $50$ students combined?

A software engineering team recorded the number of technical bugs resolved daily over a period of $20$ days. The results are summarized in the frequency table below:

What is the positive difference between the mean and the median number of bugs resolved daily during this $20$-day period?

A technology company evaluated the annual performance scores of its employees across three departments: Marketing, Engineering, and Customer Support.

- The Marketing department has $20$ employees, with a mean performance score of $92$.
- The Engineering department has twice as many employees as the Marketing department, with a mean performance score of $86$.
- The Customer Support department has $10$ more employees than the Marketing department.
- The overall mean performance score across all employees in all three departments combined is $84$.

What is the mean performance score for the Customer Support department?

An artisanal bakery prepares a specialty flour blend consisting of rye, oat, and wheat flour. By weight, $\frac{3}{10}$ of the blend is rye flour and $0.45$ of the blend is oat flour. The remaining portion of the blend is wheat flour. If a single batch of the blend contains $4.5$ pounds of wheat flour, what is the total weight, in pounds, of the flour blend prepared for the batch?

An architectural design firm is constructing a scale model of a commercial building. On the model, a rectangular conference room measures $6\text{ inches}$ in length and $4\text{ inches}$ in width. If the actual length of the conference room is $45\text{ feet}$, what is the actual area, in square feet, of the conference room?

A commercial bakery uses flour, sugar, and cocoa powder in a weight ratio of $5 : 3 : 2$ to make a chocolate cake base. To create a specialty low-sugar version, the baker decreases the amount of sugar by $30\%$ and adds that exact reduced weight to the flour, leaving the amount of cocoa powder unchanged. What is the ratio of flour to sugar in the new specialty batch?

A community theater group allocates a total budget of $d$ dollars to purchase LED stage lighting fixtures. Each fixture costs $\$145$. If the theater group purchases exactly $12$ fixtures using the total allocated budget, which of the following equations can be solved to find $d$?

A track and field athlete recorded the following distances, in meters, for 5 long jump trials during a training session: $5.8$, $6.2$, $5.5$, $6.5$, and $6.0$. The coach requires the athlete to achieve an overall mean distance of exactly $6.1$ meters across $6$ trials. What distance, in meters, must the athlete jump on the 6th trial to reach this target mean?