Grade 7 Word Problems Set 1 worksheet with math exercises on percentages, fractions, and real-world applications.

Here’s the step-by-step solution to each of the 5 Grade 7 word problems:

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Problem 1:
> Kara was interested in going to the mall to buy some new clothes. Once she got there she purchased two shirts that cost $13.42 total. If she started out with $40.00, what percentage of her money did she spend?

✔ Solution:

To find the percentage spent:
> (Amount spent ÷ Total money) × 100

So:
> ($13.42 ÷ $40.00) × 100 = ?

First, divide:
> 13.42 ÷ 40 = 0.3355

Then multiply by 100:
> 0.3355 × 100 = 33.55%

✔ Answer: 33.55%

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Problem 2:
> There are 90 people voting in a school election. There were two parties. 35% of the students voted for the red party. How many students voted for the blue party? Express your answer as a numeral, not as a percentage.

✔ Solution:

If 35% voted for the red party, then the rest voted for the blue party:
> 100% – 35% = 65%

Now calculate 65% of 90:
> 0.65 × 90 = 58.5

Wait — we can’t have half a person! But since this is a math problem, and percentages can result in decimals, let’s check if we misread.

Actually, let’s re-read: “There are 90 people voting” — so total voters = 90.

Red party: 35% of 90 = 0.35 × 90 = 31.5

That’s also not a whole number — but again, maybe it’s acceptable in this context, or perhaps we should assume rounding? However, the problem says “express as a numeral,” and doesn’t specify whole numbers.

But 31.5 voters doesn’t make sense practically. Let’s check: 35% of 90 is exactly 31.5? That suggests either the problem has an error, or we’re expected to accept decimal answers.

Alternatively — maybe the question expects us to realize that if 35% voted red, then 65% voted blue, and 65% of 90 is 58.5.

But since you can’t have half a voter, perhaps the problem intends for us to use exact math.

Let’s go with the math as given.

Blue party voters = 90 – (35% of 90) = 90 – 31.5 = 58.5

However, in real-world contexts, we’d expect whole numbers. Since the problem doesn’t specify rounding, and says “express as a numeral,” we’ll give the exact value.

✔ Answer: 58.5

*(Note: In classroom settings, sometimes problems like this are designed to test decimal understanding, even if impractical.)*

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Problem 3:
> Two of these numbers are the same value, which ones are they? 40%, .44, ¼, .04, 4/10?

✔ Solution:

Convert all to decimals for easy comparison:

- 40% = 40 ÷ 100 = 0.40
- .44 = 0.44
- ¼ = 1 ÷ 4 = 0.25
- .04 = 0.04
- 4/10 = 4 ÷ 10 = 0.4

So now compare:
- 0.40 (from 40%)
- 0.44
- 0.25
- 0.04
- 0.4 (from 4/10)

Notice: 0.40 and 0.4 are the same value → 40% and 4/10 are equal.

✔ Answer: 40% and 4/10

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Problem 4:
> Kara wanted to earn a 90% for her overall history grade. During the course she has to take 5 tests. So far, she has only taken 4 tests. Her exam scores for the tests are as follows; 85, 83, 99, 95. If Kara wants to ensure she will receive a 90%, what is the minimum score on the 5th test that she can receive?

✔ Solution:

She wants an average of at least 90 over 5 tests.

Total points needed for 90 average:
> 90 × 5 = 450

Current total from 4 tests:
> 85 + 83 + 99 + 95 = let’s add:

85 + 83 = 168
168 + 99 = 267
267 + 95 = 362

So, she needs:
> 450 – 362 = 88

✔ Answer: 88

*(She must score at least 88 on the 5th test to get a 90 average.)*

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Problem 5:
> Ellen was interested in selling her father’s tools for their garage sale. Her father said she could sell 43% of the total tools. If Ellen ended up selling 12 tools, how many tools did Ellen’s father begin with?

✔ Solution:

Let total tools = x

She sold 43% of x = 12

So:
> 0.43x = 12

Solve for x:
> x = 12 ÷ 0.43 ≈ ?

Calculate:
> 12 ÷ 0.43 ≈ 27.906...

Since number of tools must be a whole number, and she sold *exactly* 12 tools which is 43% of total, we need to find the total such that 43% of it equals 12.

Check: Is 12 / 0.43 an integer? No.

But maybe the problem expects us to round? Or perhaps it's a trick.

Wait — 43% of total = 12 → total = 12 / 0.43 ≈ 27.906

But tools can’t be fractional. So maybe the 43% is approximate? Or perhaps we need to report the exact value.

In math problems like this, unless specified, we usually report the exact decimal or fraction.

But since the question asks “how many tools did Ellen’s father begin with?” — implying a whole number — and 43% of 28 is:

> 0.43 × 28 = 12.04 → too high

0.43 × 27 = 11.61 → too low

So no whole number gives exactly 12 at 43%.

This suggests either:
- The problem allows decimal answer (unlikely for tools)
- Or it’s a typo — maybe 40% or 50%?

But based on given info, we do the math:

✔ Answer: Approximately 27.91 tools — but since that’s impossible, perhaps the problem expects 28 as the closest whole number.

However, strictly speaking:

> x = 12 / 0.43 = 1200 / 43 ≈ 27.906976...

We can leave it as a fraction: 1200/43

But for practical purposes, and since the problem likely expects a whole number, perhaps we should consider that 43% is rounded — but the problem doesn’t say that.

Given the instructions, I think we should report the exact value.

✔ Answer: 1200/43 or approximately 27.91

But in elementary math, sometimes they expect you to round up — because you can’t have part of a tool.

If she sold 12 tools and that’s 43%, then total must be more than 27. So minimum whole number is 28.

Let’s check: 43% of 28 = 0.43×28 = 12.04 → which is slightly more than 12 — meaning if total was 28, 43% would be ~12.04, so she couldn’t have sold exactly 12 unless total was fractional.

This is a bit of a trick question.

Perhaps the problem meant 40%? Because 40% of 30 = 12.

But as written, we must go with:

✔ Final Answer: 12 ÷ 0.43 = 27.906… → so the father began with approximately 27.91 tools — but realistically, this problem may contain an error.

However, since the worksheet is for Grade 7, and often expects exact answers, let’s present the precise calculation.

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## ✔ Final Answers Summary:

1. 33.55%
2. 58.5
3. 40% and 4/10
4. 88
5. 12 ÷ 0.43 = 27.906... (or 1200/43) — though practically, this suggests a possible error in the problem.

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