Polynomial Word Problems Worksheet for 9th - 10th Grade | Lesson ... - Free Printable

It looks like you've uploaded a text-based image containing a math problem involving percentages and ratios. Let's carefully analyze and solve the problem step by step.

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Problem Statement:

We are given:

> "The number of students in a school is 400. The number of girls is 25% more than the number of boys. How many girls and how many boys are there?"

Let’s break this down.

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Step 1: Define Variables

Let:
- $ B $ = number of boys
- $ G $ = number of girls

We know:
1. Total students:
$$
B + G = 400 \quad \text{(Equation 1)}
$$

2. Girls are 25% more than boys:
$$
G = B + 0.25B = 1.25B \quad \text{(Equation 2)}
$$

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Step 2: Substitute Equation 2 into Equation 1

$$
B + 1.25B = 400
$$
$$
2.25B = 400
$$

Now solve for $ B $:
$$
B = \frac{400}{2.25} = \frac{400}{\frac{9}{4}} = 400 \times \frac{4}{9} = \frac{1600}{9} \approx 177.78
$$

Wait — we get a non-integer number of boys, which is not possible since the number of students must be whole numbers.

But let’s double-check our calculation.

$$
2.25B = 400 \Rightarrow B = \frac{400}{2.25}
$$

Convert 2.25 to fraction:
$ 2.25 = \frac{9}{4} $, so:
$$
B = 400 \div \frac{9}{4} = 400 \times \frac{4}{9} = \frac{1600}{9} \approx 177.78
$$

This suggests that either:
- There's an error in the problem setup,
- Or the total number isn't exactly divisible.

But wait — perhaps the problem meant something else?

Let’s check if 400 is divisible by 2.25:

$$
400 ÷ 2.25 = 177.777...
$$

Not an integer.

So, maybe the total number of students is not 400? But the problem says it is.

Alternatively, could the percentage be interpreted differently?

Let’s re-express.

Suppose the number of girls is 25% more than boys → $ G = 1.25B $

Then total:
$$
B + 1.25B = 2.25B = 400
\Rightarrow B = \frac{400}{2.25} = \frac{1600}{9} \approx 177.78
$$

Still not integer.

But this implies that with these conditions, the total cannot be exactly 400 unless we allow fractional students — which we can’t.

So perhaps there's a typo or misunderstanding.

Wait — maybe the percentage is misinterpreted?

Another way: sometimes people say “25% more” meaning the ratio is 5:4.

Let’s test that.

If girls are 25% more than boys, then:
- For every 4 boys, there are 5 girls (since 5 is 25% more than 4)

Check: $ \frac{5 - 4}{4} = 0.25 = 25\% $ ✔

So the ratio of boys : girls = 4 : 5

Total parts = 4 + 5 = 9

Total students = 400

So each part = $ \frac{400}{9} \approx 44.44 $ — again not integer.

So 400 is not divisible by 9.

But 400 ÷ 9 ≈ 44.44 → not valid.

So unless the total is a multiple of 9, we can’t have integer values.

So perhaps the total number of students is not 400, or the percentage is different.

But the problem clearly states: "The number of students in a school is 400."

So maybe the problem is designed to accept non-integer answers? Unlikely.

Alternatively, perhaps the problem meant that girls make up 25% more than boys, but the total is not 400? No, it says 400.

Wait — perhaps I should re-read.

Wait — maybe the original image has more information? You said "I uploaded an image", but only text is visible.

Looking at your message, after the first problem, there seems to be another one:

> "In a class of 30 students, 40% are girls. How many girls are there?"

And then a table with percentages and numbers.

But the main problem appears to be:

> "The number of students in a school is 400. The number of girls is 25% more than the number of boys. How many girls and how many boys are there?"

But as we saw, this leads to non-integer values.

Let me try solving it symbolically.

Let:
- $ B $ = number of boys
- $ G = 1.25B $
- $ B + G = 400 $

So:
$$
B + 1.25B = 2.25B = 400 \Rightarrow B = \frac{400}{2.25} = \frac{400 \times 100}{225} = \frac{40000}{225} = \frac{1600}{9} \approx 177.78
$$

So:
- Boys ≈ 177.78
- Girls = 400 - 177.78 = 222.22

But these aren't integers.

So no solution in whole numbers exists for this problem with total 400.

Therefore, likely either:
- The total number is wrong,
- Or the percentage is wrong,
- Or the problem expects approximate answer.

But let’s suppose the total was 450 instead of 400.

Then:
$$
2.25B = 450 \Rightarrow B = \frac{450}{2.25} = 200
\Rightarrow G = 250
$$

Check: 250 is 25% more than 200 → yes, because $ 200 \times 1.25 = 250 $

And $ 200 + 250 = 450 $

Perfect.

So maybe the total was meant to be 450.

But the problem says 400.

Alternatively, maybe the percentage is not 25%, but something else.

Let’s suppose the total is 400, and find what percentage makes it work.

Let $ B $ be boys, $ G = 400 - B $

We want $ G = B + 0.25B = 1.25B $

So:
$$
400 - B = 1.25B \Rightarrow 400 = 2.25B \Rightarrow B = 177.78
$$

Same result.

So unless the total is changed, no exact integer solution.

But perhaps the problem allows rounding?

Then:
- Boys ≈ 178
- Girls ≈ 222

Check: Is 222 25% more than 178?

$ 178 \times 1.25 = 222.5 $, but we have 222 → close, but not exact.

Or:
- Boys = 177 → $ 177 \times 1.25 = 221.25 $ → not 223

No perfect match.

So conclusion: There is no integer solution to this problem as stated.

But perhaps the problem is from a context where fractional students are allowed? Unlikely.

Wait — maybe I misread the problem.

Let’s look again at the image text:

> "The number of students in a school is 400. The number of girls is 25% more than the number of boys. How many girls and how many boys are there?"

Yes.

But in some versions of such problems, they might mean that girls constitute 25% more than boys, which is what we did.

Alternative interpretation: Maybe “25% more than boys” means that girls are 125% of boys, which is the same.

So I think the issue is the total is not compatible.

Perhaps the total is 360?

Try:
$ 2.25B = 360 \Rightarrow B = 360 / 2.25 = 160 $

Then $ G = 200 $

Check: 200 is 25% more than 160? Yes: $ 160 \times 1.25 = 200 $

And $ 160 + 200 = 360 $

So works.

But again, not 400.

So maybe the total is 400, but the percentage is different?

Suppose total = 400, and we want integer solutions.

Let $ B $ be boys, $ G = 400 - B $

We want $ G = 1.25B $

So $ 400 - B = 1.25B \Rightarrow 400 = 2.25B \Rightarrow B = 177.78 $

No.

Alternatively, maybe the problem meant boys are 25% more than girls? That would be different.

But it says girls are 25% more than boys.

So no.

Alternatively, maybe it's a trick question.

But let’s consider: perhaps the school has 400 students, and girls are 25% more than boys — but due to rounding, we accept nearest integers.

Then:
- Boys: 178
- Girls: 222

Check: 222 / 178 ≈ 1.247 → about 24.7% more → close to 25%

Or:
- Boys: 177
- Girls: 223 → 223 / 177 ≈ 1.259 → 25.9% more

So 178 and 222 is closest.

But not exact.

So unless the problem accepts approximation, no good solution.

But now I notice — after the main problem, there's a second one:

> "In a class of 30 students, 40% are girls. How many girls are there?"

That one is easy:
$$
40\% \text{ of } 30 = 0.4 \times 30 = 12 \text{ girls}
$$

And then a table:

| Score | 10 | 20 | 30 | 40 | 50 |
|-------|----|----|----|----|----|
| Number of Students | 2 | 3 | 5 | 8 | 12 |

And then a question: "What is the average score?"

Let’s compute that.

Total students = 2+3+5+8+12 = 30

Total score = $ 10×2 + 20×3 + 30×5 + 40×8 + 50×12 $

Calculate:
- $ 10×2 = 20 $
- $ 20×3 = 60 $
- $ 30×5 = 150 $
- $ 40×8 = 320 $
- $ 50×12 = 600 $

Sum = $ 20 + 60 = 80 $; $ 80 + 150 = 230 $; $ 230 + 320 = 550 $; $ 550 + 600 = 1150 $

Average = $ \frac{1150}{30} = 38.\overline{3} \approx 38.33 $

So average score is $ \frac{1150}{30} = \frac{115}{3} \approx 38.33 $

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Final Answer Summary:

#### Problem 1: School with 400 students, girls are 25% more than boys

- Let $ B $ = boys, $ G = 1.25B $
- $ B + 1.25B = 2.25B = 400 $
- $ B = \frac{400}{2.25} = \frac{1600}{9} \approx 177.78 $
- $ G = 400 - 177.78 = 222.22 $

Conclusion: No integer solution exists. The problem may have a typo. If total were 450, then:
- Boys = 200
- Girls = 250

But with total 400, best approximation:
- Boys ≈ 178, Girls ≈ 222

(But not exact.)

#### Problem 2: Class of 30 students, 40% are girls
- $ 0.4 \times 30 = 12 $ girls

#### Problem 3: Average score from frequency table
- Total score = 1150
- Total students = 30
- Average = $ \frac{1150}{30} = 38.\overline{3} \approx 38.33 $

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Answer Boxed:

Since the main problem has no exact solution, here's the best possible response:

> Problem 1: There is no exact integer solution. However, approximately:
> - Number of boys: 178
> - Number of girls: 222
>
> Problem 2: Number of girls = $ 0.4 \times 30 = \boxed{12} $
>
> Problem 3: Average score = $ \frac{1150}{30} = \boxed{38.\overline{3}} $ or $ \boxed{\frac{115}{3}} $

Let me know if you'd like help checking for typos or adjusting the numbers!