Let's solve each problem step by step and write the correct
algebraic expressions for each sentence.
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1) Peter has 100 dollars. His mother gives him x dollars more. How many dollars does he have now?
- Peter starts with
100 dollars.
- He receives
x more dollars.
- Total = 100 + x
✔ Answer: $ 100 + x $
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2) Maria has c boxes of 10 pencils. The teacher gives her another 20 pencils. How many pencils does she have altogether?
- Each box has 10 pencils → $ c $ boxes = $ 10c $ pencils
- Teacher gives 20 more pencils
- Total = $ 10c + 20 $
✔ Answer: $ 10c + 20 $
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3) John bought z hamburgers at $3 each and paid with a 20 dollar note. How much change did he get?
- Cost of one hamburger = $3
- So, total cost = $ 3z $
- He paid with $20
- Change = $ 20 - 3z $
✔ Answer: $ 20 - 3z $
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4) I have 200 marbles and divide them among t girls. How many marbles will each girl get?
- Total marbles = 200
- Number of girls = $ t $
- Marbles per girl = $ \frac{200}{t} $
✔ Answer: $ \frac{200}{t} $
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5) Peter is x years old. His dad is 4 times older than him. How old is his dad?
- Peter’s age = $ x $
- Dad is
4 times older → This means dad’s age = $ 4x $
> Note: "4 times older" is often interpreted as
4 times as old, so $ 4x $. (Some may confuse it with "4 times as old as", but in standard math contexts, it means multiplication.)
✔ Answer: $ 4x $
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6) John earns x dollars per hour. Petra earns 2 dollars per hour more than him. How much do they earn altogether per hour?
- John's rate = $ x $
- Petra's rate = $ x + 2 $
- Together: $ x + (x + 2) = 2x + 2 $
✔ Answer: $ 2x + 2 $
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7) I have 3 boxes of x paperclips. If I use 100 paperclips, how many of them will I have left?
- 3 boxes × $ x $ paperclips each = $ 3x $ paperclips
- Use 100 → Remaining = $ 3x - 100 $
✔ Answer: $ 3x - 100 $
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8) Indy has x erasers and y pencils. How many erasers and pencils does Indy have?
- Erasers = $ x $
- Pencils = $ y $
- Total items = $ x + y $
✔ Answer: $ x + y $
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✔ Final Answers:
1. $ 100 + x $
2. $ 10c + 20 $
3. $ 20 - 3z $
4. $ \frac{200}{t} $
5. $ 4x $
6. $ 2x + 2 $
7. $ 3x - 100 $
8. $ x + y $
These are algebraic expressions that represent each situation. Let me know if you'd like to evaluate any with numbers!
Parent Tip: Review the logic above to help your child master the concept of writing algebraic expressions worksheet.
