Ratios and Proportions worksheet with practice problems and examples.

Let’s solve each problem one by one, step by step.

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Problem 1: Find the missing values in similar triangles.

We’re told two triangles are similar — that means their sides are proportional (same ratios).

First triangle has sides:
- 24 cm
- 36 cm
- x cm

Second triangle has sides:
- y cm
- z cm
- 50 cm

And we’re told: “The perimeter of the first triangle is 90 cm.”

So let’s find x first.

Perimeter = sum of all sides → 24 + 36 + x = 90
→ 60 + x = 90
→ x = 90 - 60 = 30 cm

Now, since the triangles are similar, the ratios of corresponding sides must be equal.

We need to match up the sides. The largest side in the first triangle is 36? Wait — actually, 36 and 30 and 24 — so 36 is biggest? No — wait, 36 > 30 > 24. But second triangle has a side of 50 — which is bigger than any in first triangle. So maybe 50 corresponds to the largest side of first triangle? Let’s check.

Actually, looking at the diagram (even though we can’t see it, from context), usually the sides are listed in order or matched by position. But here, the problem says:

“Find the missing values” and gives equations:

Equation A: 24 / y = 36 / z = 30 / 50

Wait — that makes sense! Because if the third side of first triangle is 30, and third side of second is 50, then ratio is 30/50 = 3/5.

So scale factor from first to second triangle is 50/30 = 5/3? Or vice versa?

Actually, if 30 corresponds to 50, then the ratio of first triangle to second triangle is 30:50 = 3:5.

That means every side in first triangle multiplied by 5/3 gives the corresponding side in second triangle.

So:

y corresponds to 24 → y = 24 × (5/3) = (24÷3)×5 = 8×5 = 40

z corresponds to 36 → z = 36 × (5/3) = (36÷3)×5 = 12×5 = 60

Check: Perimeter of second triangle: 40 + 60 + 50 = 150. Ratio of perimeters should also be 3:5 → 90:150 = 3:5 ✔️

✔ So for Problem 1:
x = 30 cm, y = 40 cm, z = 60 cm

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Problem 2: Solve the proportions.

These are simple proportion problems — cross-multiply and solve.

A. 5/x = 12/30

Cross multiply: 5 × 30 = 12 × x
→ 150 = 12x
→ x = 150 ÷ 12 = 12.5

Or as fraction: 150/12 = 25/2 = 12.5

B. 7/8 = 21/y

Cross multiply: 7 × y = 8 × 21
→ 7y = 168
→ y = 168 ÷ 7 = 24

C. 3/4 = 9/z

Cross multiply: 3 × z = 4 × 9
→ 3z = 36
→ z = 12

D. 4/5 = x/3

Cross multiply: 4 × 3 = 5 × x
→ 12 = 5x
→ x = 12/5 = 2.4

E. (x - 2)/3 = 4/6

Simplify right side: 4/6 = 2/3

So: (x - 2)/3 = 2/3

Multiply both sides by 3: x - 2 = 2
→ x = 4

F. 5/(x + 1) = 10/12

Simplify right side: 10/12 = 5/6

So: 5/(x+1) = 5/6

Since numerators are same, denominators must be equal:
x + 1 = 6
→ x = 5

✔ Answers for Problem 2:
A. 12.5
B. 24
C. 12
D. 2.4
E. 4
F. 5

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Problem 3: Jack and Jill shared water in ratio 3:7. Total = 5000 mL. How much did each get?

Ratio 3:7 means total parts = 3 + 7 = 10 parts

Each part = 5000 ÷ 10 = 500 mL

Jack gets 3 parts → 3 × 500 = 1500 mL

Jill gets 7 parts → 7 × 500 = 3500 mL

Check: 1500 + 3500 = 5000 ✔️

✔ Answer: Jack got 1500 mL, Jill got 3500 mL

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Problem 4: Harry worked 7 hours, Michael worked 11 hours. Earned $1800 together. Split according to work done.

Total hours = 7 + 11 = 18 hours

Harry’s share: (7/18) × 1800
= 7 × 100 = $700

Michael’s share: (11/18) × 1800
= 11 × 100 = $1100

Check: 700 + 1100 = 1800 ✔️

✔ Answer: Harry gets $700, Michael gets $1100

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Problem 5: Lisa earns $200 more than Jackson. Jackson earns $1200 less than Scott. Total earned = $4200. Find how much each earned.

Let’s assign variables.

Let Jackson’s earnings = J

Then Lisa = J + 200

Scott = J + 1200 (because Jackson earns $1200 less than Scott → Scott = Jackson + 1200)

Total: J + (J + 200) + (J + 1200) = 4200

Combine: 3J + 1400 = 4200

Subtract 1400: 3J = 2800

Divide by 3: J = 2800 ÷ 3 ≈ 933.33... Hmm, not whole number? Let me double-check.

Wait — maybe I misread.

“Lisa earns $200 more than Jackson” → L = J + 200

“Jackson earns $1200 less than Scott” → J = S - 1200 → so S = J + 1200 ✔️

Total: L + J + S = 4200
→ (J+200) + J + (J+1200) = 4200
→ 3J + 1400 = 4200
→ 3J = 2800
→ J = 2800 / 3 = 933.333...

But money can be in cents? Maybe it’s okay? But let’s check if problem meant something else.

Wait — perhaps “Jackson earns $1200 less than Scott” means Scott earns $1200 more than Jackson — yes, that’s what I did.

Maybe the numbers are wrong? Or maybe I made a mistake.

Wait — let’s try assigning Scott as variable.

Let Scott = S

Then Jackson = S - 1200

Lisa = Jackson + 200 = (S - 1200) + 200 = S - 1000

Total: S + (S - 1200) + (S - 1000) = 4200
→ 3S - 2200 = 4200
→ 3S = 6400
→ S = 6400 / 3 ≈ 2133.33

Still fractional.

Wait — maybe the problem has a typo? Or perhaps I misread.

Looking back: “Lisa earns $200 more than Jackson, while Jackson earns $1200 less than Scott. If they earn $4200 altogether...”

Perhaps it’s $4200 total — but with these numbers, it doesn’t divide evenly.

Wait — let me calculate numerically:

If J = 2800/3 ≈ 933.33

L = 933.33 + 200 = 1133.33

S = 933.33 + 1200 = 2133.33

Sum: 933.33 + 1133.33 + 2133.33 = let’s add:

933.33 + 1133.33 = 2066.66

2066.66 + 2133.33 = 4199.99 ≈ 4200 — close enough, rounding error.

So exact fractions:

J = 2800/3 = 933 1/3

L = 2800/3 + 200 = 2800/3 + 600/3 = 3400/3 = 1133 1/3

S = 2800/3 + 1200 = 2800/3 + 3600/3 = 6400/3 = 2133 1/3

But maybe the problem expects decimal or fraction?

Alternatively — perhaps I misinterpreted “Jackson earns $1200 less than Scott”.

Another way: Maybe “Jackson earns $1200 less than Scott” means Scott = Jackson + 1200 — which is what I did.

Perhaps the total is $4200, and we have to accept fractional dollars? Unlikely for this level.

Wait — let me re-read the problem carefully.

“Lisa earns $200 more than Jackson, while Jackson earns $1200 less than Scott. If they earn $4200 altogether, how much does each person earn?”

Perhaps there’s a different interpretation.

What if “Jackson earns $1200 less than Scott” means Jackson = Scott - 1200 — same as before.

Maybe the $200 and $1200 are switched? Or total is different?

Alternatively, let’s assume the numbers are correct and proceed with fractions.

But let’s try solving again:

Set Jackson = x

Lisa = x + 200

Scott = x + 1200

Total: x + x+200 + x+1200 = 3x + 1400 = 4200

3x = 2800

x = 2800 ÷ 3 = 933.333...

So unless the problem has a typo, this is the answer.

But let’s check if 2800 is divisible by 3? 2+8+0+0=10, not divisible by 3 — so no.

Wait — perhaps “$4200” is a typo and should be $4200? Or maybe $4500?

If total were $4500, then 3x + 1400 = 4500 → 3x=3100 → still not integer.

If total were $4200, and we want integers, perhaps the differences are different.

Another thought: Maybe “Jackson earns $1200 less than Scott” means Scott earns $1200, and Jackson earns less? No, that doesn’t make sense.

Perhaps “earns $1200 less than Scott” means Jackson = Scott - 1200, which is standard.

I think we have to go with the math.

So:

Jackson: $ \frac{2800}{3} = 933.\overline{3} $

Lisa: $ \frac{3400}{3} = 1133.\overline{3} $

Scott: $ \frac{6400}{3} = 2133.\overline{3} $

But since this is likely a school problem, perhaps I made a mistake in setup.

Wait — let’s read once more: “Lisa earns $200 more than Jackson, while Jackson earns $1200 less than Scott.”

So:

L = J + 200

J = S - 1200 → S = J + 1200

Yes.

Total L + J + S = (J+200) + J + (J+1200) = 3J + 1400 = 4200

3J = 2800

J = 2800/3

Perhaps the problem meant “Scott earns $1200 more than Jackson” — same thing.

Or maybe “Lisa earns $200 more than Scott”? No, it says Jackson.

Another idea: Perhaps “Jackson earns $1200 less than Scott” means the difference is 1200, but Scott could be less? No, “less than” implies Jackson < Scott.

I think we have to accept the fractional answer, or perhaps the total is $4200 and it's fine.

But let’s calculate numerically:

Jackson: 933.33

Lisa: 1133.33

Scott: 2133.33

Sum: 933.33 + 1133.33 = 2066.66; +2133.33 = 4199.99 — due to rounding, but exactly 4200.

So in dollars and cents:

Jackson: $933.33

Lisa: $1133.33

Scott: $2133.34 (to make sum 4200)

But 933.33 + 1133.33 = 2066.66; 4200 - 2066.66 = 2133.34

But 2133.34 - 933.33 = 1200.01 — not exact.

Better to use fractions.

Jackson: 2800/3 = 933 1/3

Lisa: 3400/3 = 1133 1/3

Scott: 6400/3 = 2133 1/3

Sum: (2800 + 3400 + 6400)/3 = 12600/3 = 4200 ✔️

So exact amounts are:

Jackson: $933 \frac{1}{3}$

Lisa: $1133 \frac{1}{3}$

Scott: $2133 \frac{1}{3}$

But since this is unusual, perhaps the problem has a typo. However, based on given info, this is correct.

Maybe "earns $1200 less" means something else, but I think it's correct.

For now, I'll go with this.

✔ Answer for Problem 5:
Jackson: $933.33 (or 933 1/3)
Lisa: $1133.33 (or 1133 1/3)
Scott: $2133.33 (or 2133 1/3)

But to write neatly:

Jackson: $\frac{2800}{3}$ dollars
Lisa: $\frac{3400}{3}$ dollars
Scott: $\frac{6400}{3}$ dollars

Or approximately:

Jackson: $933.33
Lisa: $1133.33
Scott: $2133.34 (adjusted to sum to 4200)

But strictly speaking, with fractions, it's exact.

In many textbooks, they might expect the fractional form or assume integer, but here it's not integer.

Perhaps I misread the total. Let me double-check the user input.

User wrote: "If they earn $4200 altogether"

And "Lisa earns $200 more than Jackson, while Jackson earns $1200 less than Scott."

Yes.

Another possibility: "Jackson earns $1200 less than Scott" might mean Scott = Jackson - 1200? But that would mean Scott earns less, which contradicts "less than".

No, "A earns X less than B" means A = B - X.

So Jackson = Scott - 1200.

I think it's correct.

So I'll box the fractional answers.

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Final Answers Summary:

Problem 1:
x = 30 cm, y = 40 cm, z = 60 cm

Problem 2:
A. 12.5
B. 24
C. 12
D. 2.4
E. 4
F. 5

Problem 3:
Jack: 1500 mL, Jill: 3500 mL

Problem 4:
Harry: $700, Michael: $1100

Problem 5:
Jackson: $\frac{2800}{3}$ or $933.\overline{3}$
Lisa: $\frac{3400}{3}$ or $1133.\overline{3}$
Scott: $\frac{6400}{3}$ or $2133.\overline{3}$

But for Problem 5, since it's money, perhaps write as decimals rounded to nearest cent, but sum may not be exact. To be precise, keep as fractions.

However, in context, maybe the problem intended different numbers, but based on given, this is it.

Perhaps "Jackson earns $1200 less than Scott" means the amount Jackson earns is 1200 less, so if Scott is S, Jackson is S - 1200, same as before.

I think we have to proceed.

So for final answer, I'll list them clearly.

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Final Answer:
Problem 1: x = 30 cm, y = 40 cm, z = 60 cm
Problem 2: A. 12.5, B. 24, C. 12, D. 2.4, E. 4, F. 5
Problem 3: Jack got 1500 mL, Jill got 3500 mL
Problem 4: Harry earned $700, Michael earned $1100
Problem 5: Jackson earned $\frac{2800}{3}$ dollars ($933.33), Lisa earned $\frac{3400}{3}$ dollars ($1133.33), Scott earned $\frac{6400}{3}$ dollars ($2133.33) — note: these are exact fractions; in decimal, they repeat, but sum to $4200 exactly when using fractions.