Writing Algebraic Expressions - Worksheets - Free Printable

Let’s go through each problem one by one. We’re writing expressions — that means using numbers, letters (variables), and math symbols to show what’s happening in each situation.

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1. You are going to an amusement park. It costs $15 to get in and $2 for each ride, r.

- You pay $15 no matter what.
- Then you pay $2 for every ride → that’s 2 × r = 2r
- Total cost: 15 + 2r

✔ Expression: 15 + 2r

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2. Miles makes $14 per hour but has to pay $55 for his cell phone bill.

- He earns 14 dollars for each hour he works → let’s say he works h hours → 14h
- But he must subtract $55 for the bill
- So money left: 14h - 55

✔ Expression: 14h - 55

*(Note: The problem doesn’t specify a variable for hours, so we use “h” as a reasonable choice.)*

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3. Olivia bought 8 bags of fruit at the farmer’s market. She put a apples and b bananas in each bag.

- Each bag has a apples → 8 bags × a = 8a apples total
- Each bag has b bananas → 8 bags × b = 8b bananas total
- Total fruit: 8a + 8b

✔ Expression: 8a + 8b

*(You could also write 8(a + b) — both are correct!)*

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4. Ms. Baynes has $70 and spends $4 on each of y books.

- She starts with $70
- Spends 4 × y = 4y on books
- Money left: 70 - 4y

✔ Expression: 70 - 4y

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5. Anna and her brother were collecting seashells. She collected s shells and her brother collected twice as much.

- Anna: s shells
- Brother: 2 × s = 2s shells
- Together: s + 2s = 3s

✔ Expression: s + 2s or simplified 3s

*(We’ll keep it as s + 2s since the question says “write an expression,” not simplify.)*

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6. Carlos and Brandon had p pencils and e erasers. They combined these and split them equally.

- Total items: p + e
- Split between 2 people → divide by 2
- Each gets: (p + e) ÷ 2 → written as (p + e)/2

✔ Expression: (p + e)/2

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7. Mason’s mom bought g games online. The games cost $12 each plus a $7 shipping fee.

- Cost of games: 12 × g = 12g
- Plus $7 shipping
- Total: 12g + 7

✔ Expression: 12g + 7

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8. Haley and Mia’s dad said if they combine the money they’ve saved, he would double it.

- Let’s say Haley saved H dollars, Mia saved M dollars
- Combined: H + M
- Dad doubles it: 2 × (H + M)

✔ Expression: 2(H + M)

*(If the problem expects one variable, maybe assume they saved same amount? But it doesn’t say that. So best to use two variables or just describe combining first. Since no specific amounts given, this is fine.)*

Actually — looking again, the problem doesn’t give names for how much each saved. Maybe we can use one variable? Wait — no, it says “combine the money they’ve saved” — so unless told otherwise, we should represent their savings separately.

But sometimes in these problems, they expect you to use one variable if not specified. Hmm.

Wait — actually, re-reading: “if they combine the money they’ve saved, he would double it.” It doesn’t ask for how much each has — just the final amount after doubling.

So if we let T = total they saved together, then doubled is 2T.

But the problem wants an expression based on what they saved — probably expecting us to define variables.

Since it’s ambiguous, safest is to use two variables: Let H = Haley’s savings, M = Mia’s savings → expression is 2(H + M)

Alternatively, if we assume they saved the same amount, say x each → total 2x, doubled is 4x — but that’s assuming too much.

I think 2(H + M) is best.

But wait — maybe the problem expects just one variable? Let me check other problems — most use one variable per person/item.

Actually, perhaps we can let S = total saved by both → then expression is 2S.

That might be simpler and acceptable.

Looking at grade level (probably middle school), they may accept either.

But to match style of other answers, let’s use:

Let’s say they saved a total of t dollars → then doubled is 2t.

But the problem doesn’t name the variable.

Hmm.

Actually, in many textbooks, for this type, they’d say: Let x = amount Haley saved, y = amount Mia saved → expression: 2(x + y)

I’ll go with that.

✔ Expression: 2(h + m) *(using lowercase for consistency with other problems)*

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9. Jacob makes $10 for every lawn he mows, m. He owes his brother $20.

- Earns: 10 × m = 10m
- Owes $20 → subtract that
- Net money: 10m - 20

✔ Expression: 10m - 20

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10. Rosa is making a cherry pie. She divides c cherries into 4 pies and eats the remaining 4 cherries.

- She uses some cherries for 4 pies → let’s say she puts equal amount in each pie? Not specified.
- Actually, reads: “divides c cherries into 4 pies and eats the remaining 4 cherries.”

So: total cherries = c

She uses some for pies, eats 4.

So cherries used for pies = c - 4

Then divided into 4 pies → each pie gets (c - 4)/4

But the question is: “Write an expression to represent each situation.”

What is the situation? Probably: how many cherries per pie? Or total used?

Re-read: “She divides c cherries into 4 pies and eats the remaining 4 cherries.”

The key is: she had c cherries, ate 4, so used c - 4 for the pies, and split those into 4 pies.

But the expression likely wants: how many cherries go into each pie? That would be (c - 4)/4

Or maybe total cherries used for pies: c - 4

But the phrase “divides c cherries into 4 pies” suggests she’s distributing them, and after eating 4, the rest go to pies.

I think the intended expression is for how many cherries per pie: (c - 4) ÷ 4

✔ Expression: (c - 4)/4

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Now, let’s list all final answers clearly.

Final Answer:
1. 15 + 2r
2. 14h - 55
3. 8a + 8b
4. 70 - 4y
5. s + 2s
6. (p + e)/2
7. 12g + 7
8. 2(h + m)
9. 10m - 20
10. (c - 4)/4