Grade 8 Algebraic Modeling Worksheet
This worksheet focuses on algebraic modeling for Grade 8 students, covering translating word problems into algebraic expressions and equations, solving them, and interpreting solutions.
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Standards
Topics
Grade 8 Algebraic Modeling
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Read each question carefully and follow the instructions. Show all your work for full credit.
Translate the following phrases into algebraic expressions:
1. Five more than twice a number:
2. The product of a number and seven, decreased by three:
3. The quotient of a number and four, increased by ten:
Choose the correct equation that models each word problem:
4. A taxi charges a flat fee of $3.00 plus $2.50 per mile. If the total cost of a ride was $28.00, which equation represents the number of miles (m) traveled?
3m + 2.50 = 28
2.50m + 3 = 28
3m - 2.50 = 28
2.50m - 3 = 28
5. Sarah is saving money. She started with $50 and saves $15 each week. Which equation shows how many weeks (w) it will take her to save $200?
50w + 15 = 200
15w - 50 = 200
15w + 50 = 200
50 - 15w = 200
Solve the following word problems by first writing an algebraic equation and then solving it. Show your work.
6. A rectangle has a perimeter of 60 meters. The length is twice the width. Find the dimensions of the rectangle.
Equation:
Solution:
7. Emily bought 3 notebooks and 2 pens. Each notebook cost $4. If she spent a total of $16, how much did each pen cost?
Equation:
Solution:
Determine if the following statements are True or False:
8. The expression 'x - 5' represents 'five less than a number'.
True
False
9. If 'y' represents the cost of an item and there is a 10% discount, the new cost can be modeled as 'y - 0.10'.
True
False
10. A plant grows at a rate of 2 cm per week. It was 5 cm tall when planted. Create a graph showing the plant's height (y) over weeks (x) for the first 5 weeks.
What is the algebraic equation that models the plant's growth?