The #1 SAT Math Skill Nobody Practices
Every SAT math word problem requires the same first step: translate English into algebra. Most students jump straight to solving — but if you set up the wrong equation, you get the wrong answer no matter how good your algebra is.
This drill isolates that critical first step. Read each problem, identify what's being asked, ignore the noise, and write only the equation. Don't solve it.
💡The trap: These problems are designed to confuse you. They include extraneous numbers, reversed phrasing, and nested relationships. If you can translate these correctly, real SAT problems will feel straightforward.
How to use this page: Read each problem, write your equation on paper, then click "Show Equation" to check. Aim for under 30 seconds per problem. When you're done, try Set 2 for harder categories.
1. Find the Unknown
1
A plumber charges a service fee plus per hour. The homeowner has a coupon for off the total and mentions the job is on the 3rd floor, which the plumber notes but does not charge extra for. If the final bill after the coupon is , write an equation to find the number of hours the plumber worked.
2
Marcus is 4 years older than twice his sister Jade's age. Their cousin, who is 19, is visiting for the holidays. If Marcus is 30 years old, write an equation that could be used to find Jade's age.
3
Two trains leave the same station at the same time traveling in opposite directions. Train A travels at 65 mph and Train B travels at 80 mph. A third train departs 2 hours later at 90 mph heading north. After how many hours are Trains A and B 435 miles apart? Write the equation.
4
A phone plan costs per month for the first 3 months, then per month after that. The activation fee is , and the phone case () was purchased separately. If the total cost of the plan alone for 12 months is , write an equation to find the monthly rate after the promotional period.
5
The number of hours a student studied last week exceeds the tutoring fee in dollars divided by 15 by exactly 2. The student's GPA is 3.4. If the tutoring fee was , and the student studied for 8 hours, write the equation.
2. Two Things Changing
6
A candle burns at a constant rate. When first lit, it was 12 inches tall. After burning for 3 hours, it was 9.75 inches tall. The candle was purchased in a pack of 6, but only one is being used. Write a linear equation for the candle's height in terms of hours burned .
7
A rental car company charges a flat daily fee plus a per-mile charge. On a day trip, Priya drove 120 miles and was charged . On a weekend trip, she drove 300 miles and was charged . Her insurance covers up to in rental fees per year. Write a linear equation relating total cost to miles driven .
8
A swimming pool is being drained. The pool holds 15,000 gallons when full, but it was only 80% full when draining began. Water drains at a constant rate of 250 gallons per hour. Write an equation for the amount of water remaining after hours of draining.
9
The temperature inside an oven increases linearly after being turned on. At the moment it's turned on, the oven is at room temperature, 68°F. After 4 minutes, it reaches 428°F. The oven's maximum setting is 550°F. Write a linear equation for the temperature after minutes.
3. Two Rules, Two Unknowns
10
A theater sells adult tickets for and child tickets for . On Saturday, 340 total tickets were sold, and the revenue was . The theater has 400 seats, but not all were filled. Write a system of equations that could be used to find the number of adult and child tickets sold.
11
A chemist mixes a 40% acid solution with a 15% acid solution to create 10 liters of a 25% acid solution. The lab temperature is 72°F. Write a system of equations to find the amount of each solution used.
12
The sum of two numbers is 54. The larger number is 3 less than twice the smaller number. A third number in the set is 17. Write a system of equations to find the first two numbers.
13
A farm has chickens and cows. There are 50 animals total and 140 legs total. The farm also has 3 ponds and 12 acres of land. Write a system of equations to determine the number of chickens and cows.
4. Ratios & Proportions
14
A map uses a scale where 2.5 centimeters represents 40 kilometers. The map is printed on A3 paper (29.7 cm × 42.0 cm). Two cities are 7.5 centimeters apart on the map. Write an equation to find the actual distance between the cities.
15
A recipe calls for 3 cups of flour for every 2 cups of sugar. A baker wants to make a batch using 9 cups of flour. She already has 10 cups of sugar in her pantry. Write an equation to find how many cups of sugar the recipe requires.
16
A car travels 210 miles on 6 gallons of gas. The gas tank holds 14 gallons when full, but it was only half full at the start of the trip. For a 385-mile road trip, write an equation to find the number of gallons needed.
17
In a class of 35 students, the ratio of students who prefer math to those who prefer science is 4 to 3. Five students were absent during the survey, but all 35 are counted in the ratio. Write an equation to find the number of students who prefer math.
5. Percent Traps
18
A store marks up a wholesale item by 60%, then offers a 25% sale on the marked-up price. The wholesale cost is . A loyalty card gives an additional off, applied after the sale price. Write an equation for the final price the customer pays.
19
A city's population grew by 15% in the first decade, then declined by 10% of the new population in the second decade. The city covers 42 square miles. If the original population was , write an expression for the population after both decades.
20
A laptop originally priced at has a 20% discount applied first, then an 8% sales tax is applied to the discounted price. A gift card is applied after tax. Write an equation for the amount the customer pays.
Nice work — 20 down!
You just built the foundation: linear equations, systems, ratios, and percentages. Ready to level up? Set 2 brings inequalities, quadratics, and exponentials.
Keep going — Set 2 →