Variation Word Problems Worksheets | Direct, Inverse, Joint ... - Free Printable

Let’s solve each problem step by step.

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Problem 1:
Tullahassee Inc. is known for making high quality toys. If they take 8 days to stitch 90 suits, how long will it take them to complete an order of 180 suits?

This is a direct variation: more suits → more time (assuming same rate).

If 90 suits take 8 days, then 180 suits (which is double) should take double the time.

→ 8 × 2 = 16 days

✔ Check: Rate = 90 suits / 8 days = 11.25 suits/day
Time for 180 suits = 180 ÷ 11.25 = 16 days → Correct.

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Problem 2:
A popular hair salon disbursed daily wages of $4144.80 equally among 8 shampooers. Determine the number of shampooers that were employed at the salon on the following day, if the salon paid out a total of $1132.50 in daily wages.

First, find wage per shampooer:

$4144.80 8 = $518.10 per shampooer

Now, next day total paid = $1132.50

Number of shampooers = Total paid ÷ Wage per person
= 1132.50 ÷ 518.10 ≈ ?

Let’s calculate:

518.10 × 2 = 1036.20
1132.50 - 1036.20 = 96.30 → not enough for another full person? Wait — maybe I made a mistake.

Wait — let me recalculate division:

1132.50 ÷ 518.10

Do exact division:

Multiply numerator and denominator by 100 to eliminate decimals:

113250 ÷ 51810

Divide both by 10: 11325 ÷ 5181

Try dividing:

5181 × 2 = 10362
11325 - 10362 = 963 → so 2 + 963/5181 ≈ 2.187...

But that can’t be right — you can’t have partial employees.

Wait — perhaps I miscalculated the per-person wage.

Original: $4144.80 ÷ 8

Let me compute again:

4144.80 ÷ 8:

8 × 500 = 4000 → remainder 144.80
8 × 18 = 144 → remainder 0.80
8 × 0.10 = 0.80 → so total = 500 + 18 + 0.10 = 518.10 → correct.

Now 1132.50 ÷ 518.10

Use calculator-style:

518.10 × 2 = 1036.20
Subtract from 1132.50: 1132.50 - 1036.20 = 96.30

96.30 518.10 ≈ 0.1858 → so total ≈ 2.1858 → but that doesn't make sense for number of people.

Wait — maybe the problem means “equally among 8” one day, and next day total is different — but still equal pay per person? Then number of people must be integer.

Perhaps I need to check if 1132.50 is divisible by 518.10 exactly?

Let me try: 518.10 × 2.1858... no.

Alternative approach: Maybe the wage per person changed? But problem says “disbursed daily wages... equally among 8” — implies fixed rate per person? Or does it mean total divided equally that day?

Re-read: “disbursed daily wages of $4144.80 equally among 8 shampooers” → so each got 4144.80 / 8 = 518.10

Then next day, total paid = 1132.50 — assuming same rate per person, number of people = 1132.50 / 518.10

Compute precisely:

1132.50 ÷ 518.10 = ?

Let me do decimal division:

518.10 into 1132.50

Move decimal: 51810 into 113250

51810 × 2 = 103620
113250 - 103620 = 9630

Bring down 0 → 96300

51810 × 1 = 51810 → subtract → 44490

Bring down 0 → 444900

51810 × 8 = 414480 → subtract → 30420

So approximately 2.18... → but this suggests about 2.18 people — impossible.

Wait — perhaps I misread the numbers.

Check original: “$4144.80” and “$1132.50”

Maybe it's 4144.80 for 8 people → per person 518.10

Next day total 1132.50 → number of people = 1132.50 / 518.10

Let me use fractions:

4144.80 = 414480/100 = 10362/25? Better to use decimals.

Note: 518.10 × 2 = 1036.20
518.10 × 2.2 = 518.10 × 2 + 518.10 × 0.2 = 1036.20 + 103.62 = 1139.82 → too big

518.10 × 2.1 = 1036.20 + 51.81 = 1088.01
1132.50 - 1088.01 = 44.49

44.49 / 518.10 ≈ 0.0858 → so 2.1858 — still not integer.

Perhaps the problem has a typo? Or I need to round?

But the instruction says "round your answer to two decimal places" — oh! Look at top of worksheet: “Round your answer to two decimal places.”

Ah! So even if it’s number of people, we report as decimal? That seems odd, but per instructions.

So 1132.50 ÷ 518.10 = ?

Calculate:

1132.50 ÷ 518.10 = 2.18587... → rounded to two decimal places = 2.19

But that doesn’t make practical sense — however, since the worksheet says to round to two decimals, we’ll go with that.

Wait — let me confirm calculation:

518.10 × 2.19 = 518.10 × 2 + 518.10 × 0.19 = 1036.20 + 98.439 = 1134.639 → which is over 1132.50

Too high.

518.10 × 2.18 = 518.10 × 2 + 518.10 × 0.18 = 1036.20 + 93.258 = 1129.458

1132.50 - 1129.458 = 3.042 → so 2.18 + (3.042/518.10) ≈ 2.18 + 0.00587 ≈ 2.18587 → yes.

Rounded to two decimals: look at third decimal is 5, so round up → 2.19

But 2.19 gives 1134.639 > 1132.50 — inconsistency due to rounding.

Actually, when rounding the quotient, we don’t multiply back — we just compute the division and round.

So 1132.50 ÷ 518.10 = 2.18587... → to two decimal places: 2.19

I think we have to go with that per instructions.

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Problem 3:
Shaun eats six eggs a day with a protein content of 21.6 grams. Calculate his protein intake, if he consumes 9 eggs within a day.

Direct variation: more eggs → more protein.

Protein per egg = 21.6 grams ÷ 6 eggs = 3.6 grams per egg

For 9 eggs: 9 × 3.6 = 32.4 grams

✔ Check: 6 eggs → 21.6g, so 9 eggs is 1.5 times → 21.6 × 1.5 = 32.4g → correct.

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Problem 4:
Acela Express, the fastest train between Washington DC and Boston covers a distance of 455 miles in 7 hours. How many miles does the train travel in 4 hours?

Assuming constant speed.

Speed = Distance Time = 455 miles ÷ 7 hours = 65 miles per hour

In 4 hours: 65 × 4 = 260 miles

✔ Check: 7 hours → 455 miles, so per hour 65, 4 hours → 260 → correct.

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Problem 5:
Mr Green landed at JFK airport and exchanged €700 for $854 at a currency exchange store. He realized that he would need more cash and exchanged €400 more. How many dollars did he receive for the second transaction?

First, find exchange rate: €700 → $854

Rate = 854 ÷ 700 = ?

854 ÷ 700 = 1.22 dollars per euro

Check: 700 × 1.22 = 854 → yes.

So for €400: 400 × 1.22 = 488 dollars

✔ Check: 400 × 1.22 = 488 → correct.

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Now, compiling all answers:

1. 16.00 days
2. 2.19 (number of shampooers — though unusual, per rounding instruction)
3. 32.40 grams
4. 260.00 miles
5. 488.00 dollars

All rounded to two decimal places as instructed.

Final Answer:
1. 16.00
2. 2.19
3. 32.40
4. 260.00
5. 488.00