Multi-step math word problems for grades 7 and 8

Multi-Step Math Word Problems for Grades 7 and 8

Practice 7th and 8th grade math word problems that have more than one step. Includes answer key at the end.

Problem 1: Percentages Jane bought a dress for $120. The store had a sale offering a 25% discount. After the discount, she also had to pay a 6% sales tax. What was the final price of the dress?

Problem 2: Proportions If 3 kg of apples cost $12, how much would 7 kg of apples cost?

Problem 3: Algebraic Equations Solve for x: 3x+5=2x+123x+5=2x+12.

Problem 4: Geometry - Area A rectangle has a length of 12 cm and a width of 8 cm. What is the area of the rectangle?

Problem 5: Volume A cylindrical can has a radius of 5 cm and a height of 10 cm. Calculate the volume of the can. (Use π ≈ 3.14)

Problem 6: Speed and Distance A car travels at a speed of 60 km/h. How long will it take to travel a distance of 150 km?

Problem 7: Probability A box contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of drawing a red ball?

Problem 8: Ratios The ratio of boys to girls in a class is 3:4. If there are 21 boys, how many girls are there?

Problem 9: Simple Interest Calculate the simple interest earned on a principal amount of $500 at an interest rate of 5% per annum for 3 years.

Problem 10: Perimeter A square has a side length of 7 cm. What is the perimeter of the square?

Problem 11: Temperature Conversion Convert 68°F to Celsius using the formula C=59(F−32)C=95​(F−32).

Problem 12: Inequalities Solve the inequality 4x−7>54x−7>5.

Problem 13: Coordinate Geometry Find the midpoint of the line segment joining the points (2, 3) and (6, 7).

Problem 14: Percent Change The price of a book increased from $20 to $25. What is the percentage increase?

Problem 15: Function Evaluation If f(x)=2x2−3x+4f(x)=2x2−3x+4, find f(2)f(2).

Problem 16: Linear Equations Find the slope of the line passing through the points (1, 2) and (4, 8).

Problem 17: Volume of a Rectangular Prism A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 10 cm. What is its volume?

Problem 18: Surface Area Find the surface area of a cube with a side length of 4 cm.

Problem 19: Exponents Simplify 23×22x23×22.

Problem 20: Percent of a Number What is 15% of 200?

Problem 21: Time Conversion Convert 2 hours and 45 minutes to minutes.

Problem 22: Systems of Equations Solve the system of equations: 2x+y=102x+y=10 x−y=1x−y=1

Problem 23: Quadratic Equations Solve x2−5x+6=0x2−5x+6=0.

Problem 24: Mean, Median, Mode Find the mean, median, and mode of the set of numbers: 4, 8, 6, 5, 3, 4, 7.

Problem 25: Probability If you roll two six-sided dice, what is the probability of getting a sum of 7?

Problem 26: Area of a Triangle Find the area of a triangle with a base of 10 cm and a height of 5 cm.

Problem 27: Algebraic Expressions Simplify 3a+4a−2a3a+4a−2a.

Problem 28: Distance Formula Find the distance between the points (1, 2) and (4, 6) using the distance formula.

Problem 29: Volume of a Sphere Calculate the volume of a sphere with a radius of 6 cm. (Use π ≈ 3.14)

Problem 30: Discount and Sales Tax A bicycle originally costs $200. It is on sale for 20% off. After the discount, a 5% sales tax is applied. What is the final price?

Answer Key

1) $95.40
2) $28
3) x=7x=7
4) 96 cm²
5) 785 cm³
6) 2.5 hours
7) 1221​ or 50%
8) 28 girls
9) $75
10) 28 cm
11) 20°C
12) x>3x>3
13) (4, 5)
14) 25%
15) 6
16) 2
17) 400 cm³
18) 96 cm²
19) 25=3225=32
20) 30
21) 165 minutes
22) x=3,y=4x=3,y=4
23) x=2x=2 or x=3x=3
24) Mean: 5.29, Median: 5, Mode: 4
25) 1661​
26) 25 cm²
27) 5a5a
28) 5 units
29) 904.32 cm³
30) $168