Algebra: Linear Equations, Inequalities in Context

Worked Examples: SAT Strategy

Practice Questions

Level 1: Easy (Foundational SAT)

1. A plumber charges a flat call-out fee of $\$50$ and an additional $\$75$ for each hour worked. Which equation represents the total cost $C$, in dollars, for $h$ hours of work?
   • A) $C = 50h + 75$
   • B) $C = 75h + 50$
   • C) $C = 125h$
   • D) $C = 75h - 50$
2. A baker has 120 cups of flour. Every batch of cookies requires 3 cups of flour. Which equation models the number of cups of flour remaining, $F$, after baking $b$ batches of cookies?
   • A) $F = 120 + 3b$
   • B) $F = 3b - 120$
   • C) $F = 120 - 3b$
   • D) $F = 120b - 3$
3. The function $h(t) = 15 + 2.5t$ represents the height $h$, in inches, of a plant $t$ weeks after it was purchased. What is the best interpretation of the number 15 in this context?
   • A) The number of weeks the plant will survive.
   • B) The height of the plant when it was purchased.
   • C) The amount the plant grows each week.
   • D) The maximum height the plant can reach.
4. A theater can hold a maximum of 300 people. If $a$ represents the number of adults and $c$ represents the number of children attending a show, which inequality represents this constraint?
   • A) $a + c \le 300$
   • B) $a + c \ge 300$
   • C) $a - c \le 300$
   • D) $a + c = 300$
5. A gym membership costs $\$20$ per month plus a one-time joining fee of $\$45$. If Sarah has exactly $\$165$ to spend, for how many months can she afford the gym membership? (Grid-in)

Level 2: Medium (Standard SAT)

1. A catering company charges $\$15$ per guest for a standard meal and $\$25$ per guest for a premium meal. If a client has a budget of exactly $\$1,000$ and invites exactly 50 guests, which system of equations can be used to find the number of standard meals $s$ and premium meals $p$ ordered?
   • A) $s + p = 1000$ and $15s + 25p = 50$
   • B) $s + p = 50$ and $15s + 25p = 1000$
   • C) $15s + p = 50$ and $s + 25p = 1000$
   • D) $s - p = 50$ and $25s + 15p = 1000$
2. The equation $P = 100 + 20(w - 1)$ gives the profit $P$, in dollars, a salesperson makes after working for $w$ weeks, where $w \ge 1$. What is the salesperson's profit, in dollars, for the first week? (Grid-in)
3. An elevator has a maximum weight capacity of 1,500 pounds. Suppose the elevator currently contains 3 people whose average weight is 160 pounds. If a group of boxes weighing 40 pounds each is loaded into the elevator, what is the maximum number of boxes that can be safely loaded? (Grid-in)
4. A factory produces $m$ machines every hour. After 8 hours of production, 12 machines are rejected due to defects. If the factory produced 100 non-defective machines in those 8 hours, what is the value of $m$? (Grid-in)
5. The function $f(x) = 2.50x + 4.00$ defines the cost of a taxi ride where $x$ is the number of miles driven. If a passenger's total cost was $\$29.00$, how many miles did the taxi drive? (Grid-in)

Level 3: Hard (Advanced SAT)

1. A student is buying pens that cost $\$1.50$ each and notebooks that cost $\$3.00$ each. The student must buy at least 10 items in total but cannot spend more than $\$24.00$. If $p$ represents pens and $n$ represents notebooks, which system of inequalities represents this situation?
   • A) $p + n \ge 10$ and $1.50p + 3.00n \le 24$
   • B) $p + n \le 10$ and $1.50p + 3.00n \le 24$
   • C) $p + n \ge 10$ and $1.50p + 3.00n \ge 24$
   • D) $1.50p + 3.00n \ge 10$ and $p + n \le 24$
2. An internet provider charges a base fee of $\$40$ per month for up to 50 gigabytes (GB) of data. For each additional GB of data over 50, the company charges $\$2.50$. If a user's bill for a month was $\$75$, how many total GB of data did the user consume? (Grid-in)
3. At a high school, a teacher plans to buy laptops and tablets for the classroom. Laptops cost $\$400$ each and tablets cost $\$250$ each. The teacher must buy exactly 30 devices and has a budget of $\$9,000$. Assuming the teacher spends the entire budget, how many laptops were purchased? (Grid-in)
4. The equation $C = \frac{5}{9}(F - 32)$ converts a temperature in degrees Fahrenheit ($F$) to degrees Celsius ($C$). Which of the following equations correctly expresses $F$ in terms of $C$?
   • A) $F = \frac{9}{5}C + 32$
   • B) $F = \frac{9}{5}(C + 32)$
   • C) $F = \frac{5}{9}C - 32$
   • D) $F = \frac{9}{5}C - 32$
5. An artist is cutting wire to make sculptures. The wire is originally 120 inches long. The artist cuts $x$ pieces of wire that are 6 inches long and $y$ pieces of wire that are 8 inches long. If no wire is left over, which of the following could be the value of $x$?
   • A) 3
   • B) 5
   • C) 8
   • D) 11

Level 4: Very Hard (Slightly beyond SAT)

1. A farm produces both apples and peaches. On Monday, the farm sold $A$ pounds of apples for $\$1.20$ per pound and $P$ pounds of peaches for $\$1.50$ per pound. The total revenue for Monday was $\$360$. If the farm sold twice as many pounds of apples as peaches, what was the total number of pounds of fruit sold? (Grid-in)
2. The cost $C$, in dollars, to manufacture $n$ units of a certain product is given by $C = 1500 + 4.5n$. The manufacturer sells each unit for $\$12.00$. To make a profit of exactly $\$3,000$, how many units must the manufacturer produce and sell? (Assume Profit = Total Sales Revenue - Total Cost). (Grid-in)
3. In the equation $ax + by = c$, $a$, $b$, and $c$ are constants. The line represented by this equation in the $xy$-plane passes through the points $(0, 4)$ and $(6, 0)$. Which of the following could be the values of $a$, $b$, and $c$?
   • A) $a = 2, b = 3, c = 12$
   • B) $a = 4, b = 6, c = 24$
   • C) $a = 6, b = 4, c = 24$
   • D) $a = 3, b = 2, c = 12$
4. A train consists of passenger cars and cargo cars. An empty passenger car weighs 20 tons and an empty cargo car weighs 15 tons. The total weight of the empty train (excluding the locomotive) is exactly 400 tons. If there are 22 cars in total, how many more cargo cars are there than passenger cars? (Grid-in)
5. A shipping container holds $x$ small boxes and $y$ large boxes. The small boxes weigh 10 pounds each and have a volume of 2 cubic feet. The large boxes weigh 25 pounds each and have a volume of 4 cubic feet. The container is completely full with 400 cubic feet of boxes, and the total weight of the boxes is exactly 2,200 pounds. What is the value of $x$? (Grid-in)