Grade 8 Algebraic Modeling Worksheet

Grade 8 Algebraic Modeling

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?

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?

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'.

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'.

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?