8th Grade Algebra Word Problems Worksheet - Fill Online, Printable ... - Free Printable

Let’s solve each problem step by step.

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Problem 1:

> Your sister Samantha is turning 48 in April. She is 3 times older than your brother John, and twice as old as you. How old is your brother John?

We are told:
- Samantha = 48 years old
- Samantha = 3 × John → So John = 48 ÷ 3 = 16
- (Also, Samantha = 2 × you → you = 24, but we don’t need that for this question.)

✔ Check: 3 × 16 = 48 → correct.

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Problem 2:

> Every seat sold costs $8. In addition, the auditorium makes $300 per flat rate. Total made = $2772. How many seats were sold?

Total money = (money from seats) + (flat rate)

So:
Money from seats = Total - Flat rate = 2772 - 300 = 2472

Each seat = $8 → Number of seats = 2472 ÷ 8

Let’s calculate:
2472 ÷ 8
→ 8 × 300 = 2400
→ 2472 - 2400 = 72
→ 72 ÷ 8 = 9
→ So total = 300 + 9 = 309

✔ Check: 309 × 8 = 2472; 2472 + 300 = 2772 → correct.

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Problem 3:

> John buys 6 shirts. For every shirt, he gets 30% off. Normal price per shirt = $20. How much did he spend?

First, find discount per shirt:
30% of $20 = 0.30 × 20 = $6 off per shirt

So sale price per shirt = 20 - 6 = $14

He buys 6 shirts → 6 × 14 = $84

✔ Check: 6 × 20 = 120; 30% off total would be 0.30 × 120 = 36; 120 - 36 = 84 → same answer.

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Problem 4:

> Radius of circle = 4 cm. What is circumference?

Formula: Circumference = 2 × π × radius
Use π ≈ 3.14

So: 2 × 3.14 × 4 = 6.28 × 4 = 25.12 cm

✔ Check: 2πr = 2 × 3.14 × 4 = 25.12 → correct.

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Problem 5:

> American Airlines flight:
- First class ticket: $52 each
- Coach ticket: $21 each
- Total passengers: 139
- 30% are first class → rest are coach

First, find number of first class passengers:
30% of 139 = 0.30 × 139 = 41.7 → Wait! That can’t be right — people must be whole numbers.

Hold on — let’s recalculate carefully:

0.30 × 139 = ?

Break it down:
10% of 139 = 13.9
So 30% = 13.9 × 3 = 41.7

Hmm… fractional person? That suggests maybe a typo or rounding issue — but since this is a math problem, perhaps we’re meant to round? Or maybe I misread.

Wait — let me check again: “30% of the passengers composed of the first class.” Maybe it’s exact? But 139 × 0.3 = 41.7 — not possible.

Perhaps the problem expects us to use 42? Let’s see what happens if we try 42 first class.

Then coach = 139 - 42 = 97

Money from first class: 42 × 52 = let’s compute:
40×52 = 2080; 2×52=104 → total 2184

Coach: 97 × 21
100×21 = 2100; minus 3×21=63 → 2100 - 63 = 2037

Total = 2184 + 2037 = 4221

But wait — maybe they meant 30% exactly, so perhaps 139 was chosen poorly? Alternatively, maybe I should use 41.7? No — money can’t come from partial people.

Alternative idea: Maybe “30%” is approximate, and we should use nearest whole number.

Try 41 first class:

41 × 52 = 40×52 + 1×52 = 2080 + 52 = 2132
Coach = 139 - 41 = 98
98 × 21 = 100×21 - 2×21 = 2100 - 42 = 2058
Total = 2132 + 2058 = 4190

Now try 42: as above, 4221

Which one is closer to 30%?
41/139 ≈ 29.5%
42/139 ≈ 30.2% → closer to 30%

But neither is exact. However, in real-world problems like this, sometimes they expect you to go with the decimal and multiply anyway — but that doesn’t make sense for people.

Wait — perhaps I miscalculated 30% of 139?

Let me do 139 × 0.3:

139 × 3 = 417 → divide by 10 → 41.7 → yes.

Maybe the problem has a typo? Or perhaps we’re supposed to leave it as is? But no — money must be based on whole people.

Another thought: Maybe “30% of the passengers composed of the first class” means that 30% of the *seats* or something else? Unlikely.

Perhaps in context of Grade 8, they expect rounding to nearest whole number.

Since 41.7 is closer to 42, let’s go with 42 first class, 97 coach.

Total money = 42×52 + 97×21

Calculate again:

42 × 52:
40×50=2000, 40×2=80, 2×50=100, 2×2=4 → better way:
(40+2)(50+2) = 40×50 + 40×2 + 2×50 + 2×2 = 2000 + 80 + 100 + 4 = 2184 ✔️

97 × 21:
(100 - 3) × 21 = 2100 - 63 = 2037 ✔️

Total = 2184 + 2037 = 4221

Alternatively, maybe the problem intended 140 passengers? 30% of 140 = 42 exactly.

Given that, and since 139 is very close, and 42 is the logical choice, I’ll go with $4221

But let’s double-check with 41.7 — if we allow fractions (which we shouldn’t), then:

First class revenue: 41.7 × 52 = let’s compute:
40×52=2080, 1.7×52=88.4 → total 2168.4
Coach: 139 - 41.7 = 97.3
97.3 × 21 = 97×21 + 0.3×21 = 2037 + 6.3 = 2043.3
Total = 2168.4 + 2043.3 = 4211.7 → not nice.

So definitely, we must use whole numbers. Since 42 is closest to 30%, and gives clean calculation, I think the intended answer is $4221

Perhaps the problem meant 140 passengers? But it says 139. Hmm.

Wait — another approach: maybe “30% of the passengers composed of the first class” means that first class is 30%, so coach is 70%. Then:

First class: 0.3 × 139 = 41.7 → still same issue.

I think for school purposes, they expect you to round 41.7 to 42.

So final answer for #5: $4221

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Final Answers:

1. Brother John is 16 years old.
2. 309 seats were sold.
3. John spent $84.
4. Circumference is 25.12 cm.
5. Airline made $4221.

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Final Answer:
1. 16
2. 309
3. 84
4. 25.12
5. 4221