Math worksheet featuring nine word problems related to inequalities, each accompanied by a relevant icon.

Let’s go through each problem one by one. We’ll write inequalities based on the word problems, using the variables given.

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1) Farmer with fencing

He has a maximum of 50 yards of fencing for a rectangle.
Perimeter of rectangle = 2×length + 2×width → 2l + 2w
Since he can’t use more than 50 yards:
→ 2l + 2w ≤ 50

*(We can also simplify to l + w ≤ 25, but unless asked, we leave it as is.)*

✔ Final inequality: 2l + 2w ≤ 50

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2) Frazer charging phone

Max time per charge: 1 hour 30 minutes = 1.5 hours
If he charges n times, total time t must be ≤ max possible time.
So:
→ t ≤ 1.5n

✔ Final inequality: t ≤ 1.5n

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3) Quadra spending on rent and bills

She spends at least 40% of her income (i) on rent/bills.
That means remaining money (r) is at most 60% of income.
Because if she spends ≥40%, then r ≤ 60% of i.
→ r ≤ 0.6i

✔ Final inequality: r ≤ 0.6i

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4) Two-liter bottle fills cups

One bottle fills minimum 8 cups.
So b bottles fill at least 8b cups.
c = number of cups filled → c ≥ 8b
→ c ≥ 8b

✔ Final inequality: c ≥ 8b

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5) Sally reading chapters

Each chapter > 15 pages. She reads c chapters/day.
Total pages p = c × (pages per chapter)
Since each chapter is MORE than 15 pages:
→ p > 15c

✔ Final inequality: p > 15c

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6) Newton swimming lengths

Best time for 1 length = 27 seconds → that’s his FASTEST.
So for any other swim, it takes him at least 27 seconds per length.
For l lengths, time t ≥ 27 × l
→ t ≥ 27l

✔ Final inequality: t ≥ 27l

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7) Hotel stairs

f flights of stairs. Each flight has at least 12 steps.
Total steps t = f × steps per flight → since each flight ≥12, then t ≥ 12f
But note: the question says “Write an expression” — not inequality? Wait, let’s check:

> “Write an expression for the total number of steps, t, in terms of f.”

Hmm… but each flight has *at least* 12 steps — so actually, t ≥ 12f. But if they want an expression, maybe they mean minimum? Or perhaps it's still an inequality?

Looking back: Problem says “each flight has at least 12 steps” → so total steps t is at least 12f → so inequality is correct.

But wait — problem #7 says: “Write an expression...” while others say “write an inequality”. Let me double-check original text:

> 7) In a hotel there are f flights of stairs. Each flight has at least 12 steps.
> Write an expression for the total number of steps, t, in terms of f.

Ah! It says “expression”, not inequality. So even though it says “at least”, they might just want the formula assuming exactly 12? But that doesn't make sense because “at least” implies inequality.

Wait — looking at all other problems, they ask for inequalities except this one. Maybe it’s a trick? Or typo?

Actually, re-reading: “each flight has at least 12 steps” → so minimum total steps is 12f, but could be more. Since they ask for “an expression”, perhaps they expect t = 12f? But that would be incorrect because it’s not necessarily equal.

Alternatively, maybe they meant to say “write an inequality” like others. Given context, I think it’s safe to assume they want the inequality.

But let’s look again: problem 7 says “Write an expression...”, while problem 8 and 9 say “write an inequality”.

This is inconsistent. However, since each flight has *at least* 12 steps, the total steps t satisfies:

→ t ≥ 12f

I think that’s what they want, even if wording says “expression”. Probably a small error in the worksheet.

✔ Final answer: t ≥ 12f

*(If strictly "expression", then t = 12f — but that ignores “at least”. I’ll go with inequality as it makes sense mathematically.)*

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8) Frazer reading Harry Potter

Max speed: just under 36 pages/hour → so less than 36.
In h hours, pages p < 36h
→ p < 36h

✔ Final inequality: p < 36h

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9) Captain driving

Max speed: 60 mph. After h hours, miles driven m ≤ 60h
→ m ≤ 60h

✔ Final inequality: m ≤ 60h

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Now compiling all final answers:

Final Answer:
1) 2l + 2w ≤ 50
2) t ≤ 1.5n
3) r ≤ 0.6i
4) c ≥ 8b
5) p > 15c
6) t ≥ 27l
7) t ≥ 12f
8) p < 36h
9) m ≤ 60h