SAT Word Problems Practice Flashcards

Two pipes fill a tank together in 6 hours. Pipe A alone fills the tank in 10 hours. How many hours does Pipe B alone take to fill the tank?

Answer: 15

Combined rate = 1/6. Pipe A's rate = 1/10. Pipe B's rate = 1/6 − 1/10 = 2/30 = 1/15, so 15 hours.

A chemist mixes a 40% acid solution with a 10% acid solution to produce 30 liters of a 25% acid solution. How many liters of the 40% solution does she use?

Answer: 15

Let x = liters of 40% solution. 0.40x + 0.10(30 − x) = 7.5 → 0.30x = 4.5 → x = 15.

A store marks up its wholesale price by 40% to set the retail price. During a sale, it offers a 20% discount. What percent profit does the store earn over the wholesale price?

Answer: 12%

Start with wholesale = $100. Retail = $140. Sale price = $140 × 0.80 = $112. Profit = 12%.

The width of a rectangle is 6 less than its length. If the area is 91 square units, what is the perimeter?

Answer: 40

l(l − 6) = 91 → l² − 6l − 91 = 0 → (l − 13)(l + 7) = 0 → l = 13, w = 7. Perimeter = 2(13 + 7) = 40.

Working alone, Emily finishes a project in 12 days and Frank in 8 days. After 3 days working together, Frank leaves. How many more days does Emily need to finish alone?

Answer: 4.5

Together in 3 days: 3(1/12 + 1/8) = 3(5/24) = 5/8 done. Remaining = 3/8. Emily's time = (3/8)/(1/12) = 4.5 days.

The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is 27 more than the original. What is the original number?

Answer: 47

Let tens = a, units = b; a + b = 11 and 10b + a = 10a + b + 27 → b − a = 3. Solving: a = 4, b = 7. Number = 47.

A car averages 28 mph on the highway and 20 mph in the city. A driver uses 10 gallons total and drives 232 miles. How many gallons were used on the highway?

Answer: 4

h + c = 10 and 28h + 20c = 232. Substituting c = 10 − h: 8h = 32 → h = 4 gallons.