Algebra worksheet for students to practice writing expressions from word problems using variables.

Let's solve each problem step by step, writing algebraic expressions for the given sentences.

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1) I am x years old. My friend is 1 year older than me. How old will my friend be in 12 years?

- My current age: $ x $
- Friend's current age: $ x + 1 $
- In 12 years, friend's age: $ (x + 1) + 12 = x + 13 $

✔ Answer: $ x + 13 $

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2) John has y stickers. His friend gives him another 20 stickers. How many stickers does he have altogether?

- Initial stickers: $ y $
- Additional stickers: $ 20 $
- Total stickers: $ y + 20 $

✔ Answer: $ y + 20 $

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3) I bought y apples at $1 each and paid with a 100 dollar note. How much change did I get?

- Cost of y apples: $ y \times 1 = y $
- Paid: $ 100 $
- Change: $ 100 - y $

✔ Answer: $ 100 - y $

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4) I have 150 candies and divide them equally among x friends. How many candies will each friend get?

- Total candies: $ 150 $
- Number of friends: $ x $
- Candies per friend: $ \frac{150}{x} $

✔ Answer: $ \frac{150}{x} $

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5) Dad is x years old. I am 5 times younger than him. How old am I?

- "5 times younger" means my age is $ \frac{1}{5} $ of dad’s age.
- So, my age: $ \frac{x}{5} $

✔ Answer: $ \frac{x}{5} $

> Note: The phrase "5 times younger" can be ambiguous, but in math contexts, it usually means one-fifth the age.

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6) I can run x laps per hour. John can run 1 lap more per hour than I can. How many laps can we run together in 1 hour?

- My laps per hour: $ x $
- John’s laps per hour: $ x + 1 $
- Together: $ x + (x + 1) = 2x + 1 $

✔ Answer: $ 2x + 1 $

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7) I have 2 boxes of y chocolates. If I get 2 more chocolates from my friend, how many chocolates do I have in total?

- Chocolates in 2 boxes: $ 2 \times y = 2y $
- Plus 2 more: $ 2y + 2 $

✔ Answer: $ 2y + 2 $

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8) There are x blue cars, 20 red cars and 10 black cars parked in my street. How many cars are there parked altogether?

- Blue cars: $ x $
- Red cars: $ 20 $
- Black cars: $ 10 $
- Total: $ x + 20 + 10 = x + 30 $

✔ Answer: $ x + 30 $

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✔ Final Answers:

1) $ x + 13 $
2) $ y + 20 $
3) $ 100 - y $
4) $ \frac{150}{x} $
5) $ \frac{x}{5} $
6) $ 2x + 1 $
7) $ 2y + 2 $
8) $ x + 30 $

These expressions represent the solutions using letters as numbers, as required.