This worksheet helps students practice translating real-world word problems into mathematical inequalities using variables.

Let’s go through each problem one by one. We’ll write an inequality for each using the variable given and the correct symbol: >, <, ≥, ≤, or ≠.

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1) Captain has more than $2 in coins. Use variable m.

“More than” means greater than → >

So:
m > 2

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2) Bob jumps 420 cm. He jumps further than Bill. Use variable j for how far Bill jumped.

If Bob jumped further than Bill, then Bill’s jump (j) is less than 420.

So:
j < 420

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3) Cookies need to be cooked for at least 12 minutes. Use variable t.

“At least” means 12 or more → ≥

So:
t ≥ 12

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4) Minimum height to ride is 4 foot 6 inches. Use variable h.

Minimum height = you must be that tall or taller → ≥

But we need to convert 4 foot 6 inches into just feet or just inches? The problem doesn’t specify units for h, so let’s assume h is in feet.

4 foot 6 inches = 4.5 feet

So:
h ≥ 4.5

*(Alternatively, if h is in inches: 4×12 + 6 = 54 inches → h ≥ 54 — but since it says “4 foot 6 inches”, and no unit specified for h, 4.5 feet is fine.)*

We’ll go with h ≥ 4.5

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5) Newton can take a maximum of $10 spending money. Use variable s.

“Maximum of $10” means he can take $10 or less → ≤

So:
s ≤ 10

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6) Sally drinks more than half the water from a 1-liter bottle. Use variable y for how much is left.

Total = 1 liter
She drinks more than half → she drinks > 0.5 liters
So what’s left = 1 - (what she drank)

If she drank > 0.5, then what’s left < 0.5

So:
y < 0.5

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7) Flame runs 100 yards in 10 seconds. Captain takes more than twice as long. Use variable t for Captain’s time.

Twice as long as 10 seconds = 20 seconds
“More than twice as long” → t > 20

So:
t > 20

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8) Alice is more than three times as old as Bert. Bert is 6 years old. Use variable A for Alice’s age.

Three times Bert’s age = 3 × 6 = 18
Alice is more than that → A > 18

So:
A > 18

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9) Frazer can pick any number except 3. Use variable n.

“Except 3” means not equal to 3 → ≠

So:
n ≠ 3

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Final Answer:

1) m > 2
2) j < 420
3) t ≥ 12
4) h ≥ 4.5
5) s ≤ 10
6) y < 0.5
7) t > 20
8) A > 18
9) n ≠ 3