Solving proportions word problems worksheet with 10 exercises for practice.

To solve these proportion problems, we need to find the value of the variable (usually x) that makes each equation true.

Here’s how we do it:

When you see something like “a : b = c : x”, it means the ratio of a to b is the same as the ratio of c to x. We can rewrite this as a fraction:
a/b = c/x

Then we use cross multiplication:
a × x = b × c

Finally, solve for x by dividing both sides by a.

Let’s go through each problem one by one.

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Problem 1: 24 : 18 = x : 6

Rewrite as fractions:
24/18 = x/6

Cross multiply:
24 × 6 = 18 × x
144 = 18x

Divide both sides by 18:
x = 144 ÷ 18 = 8

✔ Check: 24/18 = 4/3, and 8/6 = 4/3 → Correct!

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Problem 2: 42 : 30 = 6 : x

Rewrite:
42/30 = 6/x

Cross multiply:
42 × x = 30 × 6
42x = 180

Divide by 42:
x = 180 ÷ 42 = 30/7 ≈ 4.2857, but let’s keep it as a fraction unless told otherwise.

Wait — let’s simplify first!

42/30 simplifies to 7/5 (divide numerator and denominator by 6).

So: 7/5 = 6/x → cross multiply: 7x = 30 → x = 30/7

But maybe they want decimal? Let’s check original numbers.

Actually, 42:30 reduces to 7:5, so 7:5 = 6:x → 7x = 30 → x = 30/7 ≈ 4.2857

But perhaps we should leave as fraction? The worksheet doesn’t specify. Let’s write as mixed number or decimal? Since others are whole numbers, maybe I made a mistake.

Wait — let’s double-check cross multiplication without simplifying:

42 * x = 30 * 6 → 42x = 180 → x = 180/42 = 30/7 ≈ 4.2857

Hmm. But looking at other problems, they all give whole numbers. Maybe I misread?

Wait — problem 2 says: 42 : 30 = 6 : x

Is it possible it’s 42 : 30 = x : 6? No, image shows 6 : x.

Alternatively, maybe it's written as 42/30 = 6/x → yes.

But 30/7 is not a whole number. Let me check if I copied correctly.

Looking back at user input: “2. 42 : 30 = 6 : x”

Yes. So x = 30/7. But perhaps in context, we write as decimal? Or maybe reduce?

Wait — let’s try simplifying the left side first:

42 ÷ 6 = 7, 30 ÷ 6 = 5 → so 7:5 = 6:x

Then 7/5 = 6/x → 7x = 30 → x = 30/7

Still same.

Perhaps the problem expects us to write as fraction? Or maybe I should proceed and see.

Wait — let’s look at problem 3: 4 : 8 = 36 : x → that should be easy.

Maybe for now, I’ll compute all and see which ones are clean.

Actually, let’s do all and then decide.

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Problem 3: 4 : 8 = 36 : x

4/8 = 36/x → simplify 4/8 to 1/2

So 1/2 = 36/x → cross multiply: x = 72

✔ Check: 4:8 = 1:2, 36:72 = 1:2 → Correct.

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Problem 4: 5 : 6 = x : 18

5/6 = x/18 → cross multiply: 6x = 90 → x = 15

✔ Check: 5:6 = 15:18 → divide 15 and 18 by 3 → 5:6 → Correct.

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Problem 5: 40 : 8 = x : 5

40/8 = x/5 → 5 = x/5 → x = 25

✔ Check: 40:8 = 5:1, 25:5 = 5:1 → Correct.

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Problem 6: 8 : 4 = x : 7

8/4 = x/7 → 2 = x/7 → x = 14

✔ Check: 8:4 = 2:1, 14:7 = 2:1 → Correct.

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Problem 7: 40 : 5 = x : 7

40/5 = x/7 → 8 = x/7 → x = 56

✔ Check: 40:5 = 8:1, 56:7 = 8:1 → Correct.

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Problem 8: 42 : 6 = x : 9

42/6 = x/9 → 7 = x/9 → x = 63

✔ Check: 42:6 = 7:1, 63:9 = 7:1 → Correct.

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Problem 9: 8 : 4 = x : 12

8/4 = x/12 → 2 = x/12 → x = 24

✔ Check: 8:4 = 2:1, 24:12 = 2:1 → Correct.

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Problem 10: 5 : 8 = x : 24

5/8 = x/24 → cross multiply: 8x = 120 → x = 15

✔ Check: 5:8 = 15:24 → divide 15 and 24 by 3 → 5:8 → Correct.

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Now back to Problem 2: 42 : 30 = 6 : x

We had x = 30/7 ≈ 4.2857

But let’s verify with cross multiplication again:

42 * x = 30 * 6 → 42x = 180 → x = 180 / 42

Simplify 180/42: divide numerator and denominator by 6 → 30/7

So x = 30/7 or approximately 4.29

But since all other answers are integers, maybe there’s a typo? Or perhaps we’re supposed to leave as fraction?

Wait — let me check the original image description again.

User wrote: “2. 42 : 30 = 6 : x”

Perhaps it’s meant to be 42 : 30 = x : 6? Then it would be different.

If 42:30 = x:6 → 42/30 = x/6 → 42*6 = 30x → 252 = 30x → x = 8.4 → still not integer.

Or if it’s 30:42 = 6:x → 30/42 = 6/x → 30x = 252 → x = 8.4

Still not.

Wait — what if it’s 42 : 6 = 30 : x? That would make sense.

42/6 = 30/x → 7 = 30/x → x = 30/7 — same thing.

I think we have to accept that problem 2 gives a fractional answer.

But let’s see — 30/7 is about 4.2857, but maybe in the context of the worksheet, they expect simplified fraction.

Alternatively, perhaps I miscalculated.

Another way: 42:30 simplifies to 7:5, so 7:5 = 6:x → so 7/5 = 6/x → x = (6*5)/7 = 30/7

Yes.

So for problem 2, x = 30/7

But since the instruction is to provide final answer, and all others are integers, perhaps I should list them as is.

Wait — let me check problem 1 again: 24:18 = x:6 → we got x=8

24/18 = 4/3, x/6 = 8/6 = 4/3 → good.

Problem 2: 42:30 = 7:5, 6:x = 6/(30/7) = 6 * 7/30 = 42/30 = 7/5 → yes, correct.

So x = 30/7 is correct.

But perhaps in the worksheet, they want decimal? Or maybe it's a mistake.

Since the user didn't specify, and to be accurate, I'll use exact values.

But looking at the pattern, all other problems yield integers, so maybe problem 2 is intended to be different.

Wait — let me read the user's input carefully:

"2. 42 : 30 = 6 : x"

Perhaps it's "42 : 30 = x : 6"? But user wrote "6 : x".

In the initial text: "2. 42 : 30 = 6 : x"

I think we have to go with it.

So for problem 2, x = 30/7

But to match the format, perhaps write as mixed number: 4 2/7

Or decimal? But better to keep as fraction.

However, in school worksheets, sometimes they expect simplified fraction.

But let's see the other problems — all integers.

Perhaps I should double-check the cross multiplication.

42 : 30 = 6 : x

This means 42/30 = 6/x

Cross multiply: 42 * x = 30 * 6

42x = 180

x = 180 / 42

Reduce by dividing numerator and denominator by 6: 30/7

Yes.

So I'll proceed.

Now, compiling all answers:

1. x = 8
2. x = 30/7 or approximately 4.2857 — but since others are integers, perhaps it's a typo, but I'll use 30/7
Wait — let's see if 30/7 can be left as is.

Perhaps the problem is 42 : 30 = x : 6? Let me calculate that.

If 42:30 = x:6, then 42/30 = x/6 → 42*6 = 30x → 252 = 30x → x = 8.4 = 42/5

Still not integer.

What if it's 30 : 42 = 6 : x? 30/42 = 6/x → 30x = 252 → x = 8.4

Same.

Or 42 : 6 = 30 : x → 42/6 = 30/x → 7 = 30/x → x = 30/7

Always the same.

I think it's correct, so I'll use x = 30/7 for problem 2.

But to make it neat, perhaps write as fraction.

Since the worksheet might expect whole numbers, and I have to provide final answer, let's list all as calculated.

Final answers:

1. 8
2. 30/7
3. 72
4. 15
5. 25
6. 14
7. 56
8. 63
9. 24
10. 15

But problem 2 is the only non-integer.

Perhaps in the context, they want decimal, but I think fraction is fine.

Another thought: maybe "42 : 30 = 6 : x" means 42/30 = 6/x, which is what I did.

Perhaps it's a proportion where we set up as 42/6 = 30/x, but that would be incorrect based on standard interpretation.

Standard is a:b = c:d means a/b = c/d.

So I think it's correct.

So for the final answer, I'll list them as above.

But the user asked for "the final answer", implying perhaps one answer, but there are 10 problems.

Looking back at the user's message, it's a worksheet with 10 problems, so I need to provide all 10 answers.

In the response, I should list them clearly.

Also, in the final answer section, I need to provide the answers.

So let's compile:

1. 8
2. \frac{30}{7} or 4\frac{2}{7}
3. 72
4. 15
5. 25
6. 14
7. 56
8. 63
9. 24
10. 15

For problem 2, since it's a math worksheet, and to be precise, I'll use the fraction.

But let's confirm with another approach.

The proportion 42:30 = 6:x means that the ratio is constant, so the multiplier from 42 to 6 is 6/42 = 1/7, so from 30 to x should be the same multiplier, so x = 30 * (1/7) = 30/7 — same thing.

Yes.

So I think it's correct.

Now for the final answer, I'll list all 10.

But the instruction says "provide only the final correct answer", and since there are multiple, I should list them.

Perhaps in a boxed format or something.

Since it's a worksheet, I'll write them in order.

So Final Answer:

1. 8
2. \frac{30}{7}
3. 72
4. 15
5. 25
6. 14
7. 56
8. 63
9. 24
10. 15

To make it neat, perhaps write as a list.

Since the user might expect integers, and problem 2 is odd, but I have to be accurate.

Another idea: perhaps "42 : 30 = 6 : x" is meant to be solved as 42/30 = 6/x, and x = (30*6)/42 = 180/42 = 30/7, yes.

I think it's fine.

So I'll go with that.