Ten elementary algebra word problems for 8th graders, each with a visual aid, a step-by-step solution (maximum 3
steps), and an elementary difficulty level.
Problem 1: Sarah has 3x apples, and John has x + 5 apples. If they have a total of 25 apples, how many apples does
Sarah have? (Visual: A simple diagram showing Sarah's apples and John's apples in separate groups.)
Solution: 3x + x + 5 = 25; 4x = 20; x = 5; Sarah has 3 5 = 15 apples.
Problem 2: A rectangle has a length of 2y + 3 cm and a width of y cm. If the perimeter is 24 cm, what is the width of
the rectangle? (Visual: A diagram of a rectangle with labeled sides.)
Solution: 2(2y + 3) + 2y = 24; 4y + 6 + 2y = 24; 6y = 18; y = 3; The width is 3 cm.
Problem 3: Maria bought 5 pencils and 2 erasers. Each pencil costs $x and each eraser costs $2. If she spent $19,
how much did each pencil cost? (Visual: A picture of 5 pencils and 2 erasers.)
Solution: 5x + 2(2) = 19; 5x + 4 = 19; 5x = 15; x = 3; Each pencil cost $3.
Problem 4: A train travels at a speed of x km/h. If it travels 120 km in 3 hours, what is its speed? (Visual: A simple
diagram of a train traveling a distance.)
Solution: x 3 = 120; x = 40; The speed is 40 km/h.
Problem 5: David has y marbles. He gives away 7 marbles and then doubles the remaining amount. He now has 18
marbles. How many marbles did he start with? (Visual: A diagram showing the marbles before and after the
actions.)
Solution: 2(y - 7) = 18; 2y - 14 = 18; 2y = 32; y = 16; He started with 16 marbles.
Problem 6: The sum of two consecutive numbers is 27. What are the two numbers? (Visual: A number line showing
two consecutive numbers.)
Solution: x + (x + 1) = 27; 2x + 1 = 27; 2x = 26; x = 13; The numbers are 13 and 14.
Problem 7: A triangle has angles of x, 2x, and 3x degrees. Find the value of x. (Visual: A triangle with angles
labeled x, 2x, and 3x.)
Solution: x + 2x + 3x = 180; 6x = 180; x = 30; x = 30 degrees.
Problem 8: If a number is increased by 5 and then doubled, the result is 22. What is the number? (Visual: A
flowchart showing the steps.)
Solution: 2(x + 5) = 22; 2x + 10 = 22; 2x = 12; x = 6; The number is 6.
Problem 9: The length of a rectangle is 3 times its width. If the perimeter is 32 cm, what is the length? (Visual: A
rectangle with labeled sides.)
Solution: 2(3w + w) = 32; 8w = 32; w = 4; Length = 3 4 = 12 cm.
Problem 10: A bag contains x red marbles and 4 blue marbles. If the total number of marbles is 15, how many red
marbles are there? (Visual: A bag with red and blue marbles.)
Solution: x + 4 = 15; x = 11; There are 11 red marbles.