Pre-Algebra

A high school student council must select a 3-member executive committee consisting of a President, a Vice President, and a Treasurer from a group of 6 juniors and 4 seniors. If the positions are filled sequentially at random and no student can hold more than one position, what is the probability that the President is a senior, the Vice President is a junior, and the Treasurer is a senior?

A municipal transit system tracks its monthly revenue from three fare categories: Single-Ride passes, Weekly passes, and Monthly subscriptions. Single-Ride passes account for $\frac{9}{20}$ of the total monthly revenue, and Weekly passes account for $30\%$ of the total monthly revenue. If the remaining revenue from Monthly subscriptions is $\$21,000$, what was the total monthly revenue, in dollars, for the transit system?

A community orchard initially planted apple, peach, and plum trees in the ratio $4 : 3 : 5$, respectively. After a severe frost, $12$ plum trees died and were removed from the orchard, while all apple and peach trees survived. If the new ratio of apple trees to remaining plum trees became $2 : 1$, how many total trees were originally in the orchard?

A software development team consists of $4$ front-end developers, $5$ back-end developers, and $3$ quality assurance (QA) engineers. The project manager needs to select a $3$-member subcommittee to present a new product feature. If the subcommittee must contain at least $1$ front-end developer and at least $1$ back-end developer, how many different $3$-member subcommittees can be formed?

A municipal recycling center processes $p$ tons of plastic waste per hour. During a standard 14-hour operation cycle, the center processes a total of 119 tons of plastic waste. Which of the following equations represents this scenario, and what is the value of $p$?

A local fitness center recorded the number of weekly workout sessions attended by a sample of $20$ members over the past month. The results are summarized in the frequency table below:

What is the positive difference between the mean and the median number of weekly workout sessions for these $20$ members?

A wildlife conservation team tags and monitors sea turtle nests along a coastal beach. The team divides a total of $n$ nesting data loggers equally among $6$ field researchers. If each researcher receives $14$ data loggers, which of the following equations correctly models this situation to find $n$?

An art gallery features a collection of $60$ paintings, each categorized by its medium (oil or watercolor) and its historical period ($19\text{th}$-century or $20\text{th}$-century). Among the collection, $35$ paintings are $19\text{th}$-century works, $40$ paintings are oil paintings, and $10$ paintings are $20\text{th}$-century watercolor works. If a single painting is selected at random from the collection, what is the probability that the selected painting is a $19\text{th}$-century oil painting?

A software development company allocated its annual operating budget across three departments: Engineering, Marketing, and Customer Support. Exactly $\frac{2}{5}$ of the total budget was allocated to Engineering, and $35\%$ of the total budget was allocated to Marketing. If the remaining budget of $\$45,000$ was allocated to Customer Support, what was the company's total annual operating budget?

In a wildlife sanctuary habitat, the ratio of finches to sparrows is $3 : 5$, and the ratio of sparrows to thrushes is $2 : 3$. If there are $45$ thrushes in the habitat, what is the total number of finches, sparrows, and thrushes?

A customer satisfaction survey asked $25$ patrons at a local restaurant to rate their dining experience on a scale from $1$ (poor) to $5$ (excellent). The frequency table below summarizes the ratings collected:

What is the positive difference between the mean rating and the median rating of these $25$ patrons?

A solar-powered charging station operates using two types of solar panels, Type A and Type B. The ratio of Type A panels to Type B panels installed at the station is $5 : 3$. Each Type A panel generates $24$ watt-hours of energy per hour, and each Type B panel generates $40$ watt-hours of energy per hour. If there are a total of $48$ solar panels installed at the station, how many total watt-hours of energy do all the panels generate combined in one hour?

A container holds $40$ marbles, each of which is red, blue, or green. The probability of randomly drawing a red marble from the container is $\frac{2}{5}$. Among the remaining marbles, the ratio of blue marbles to green marbles is $1:3$. If one marble is selected at random from the container, what is the probability that it is green?

A solar power plant generated a total of $480\text{ megawatt-hours (MWh)}$ of energy in one month. Of this total, $\frac{2}{5}$ was stored in battery banks, $0.35$ was supplied directly to an industrial facility, and the remaining portion was delivered to residential homes. How many megawatt-hours of energy were delivered to residential homes?

A community garden supervisor distributes a total of $d$ pounds of organic compost equally among $8$ raised garden beds. If each bed receives exactly $14.5$ pounds of compost, which of the following equations can be solved to find $d$?

A commercial diver descends at a constant rate of $2.5$ meters per second. If the diver's total change in depth after $t$ seconds is $-85$ meters, which of the following equations can be solved to find $t$?

A solar power system generated a total of $450$ kilowatt-hours (kWh) of electricity during a 3-day period. On Day 1, the system generated $\frac{2}{9}$ of the total 3-day electricity. On Day 2, it generated $40\%$ of the remaining electricity after Day 1. How many kilowatt-hours of electricity were generated on Day 3?

A community library's summer program requires participants to create a 3-book reading list consisting of exactly $1$ biography, $1$ science fiction novel, and $1$ history book selected from a featured list. The featured list contains $5$ biographies (2 of which have over $400$ pages), $6$ science fiction novels (3 of which have over $400$ pages), and $4$ history books (1 of which has over $400$ pages). If a participant selects $1$ book of each genre at random from the featured list, what is the probability that at least $1$ of the selected books has over $400$ pages? Express your answer as a decimal.