You're right to look for the "impossible/trick problem"! Let's solve each one and then identify the trick.
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1) A bike costs $350 but is reduced by 35% in a sale. What does it cost in the sale?
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Solution:
First, find 35% of $350:
`0.35 × 350 = 122.50`
Then subtract that from the original price:
`350 - 122.50 = 227.50`
✔ Answer: $227.50
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2) A bag contains some red, blue and yellow balls. 32% of the balls are blue and 44% are red. If there are 150 balls in the bag, how many are yellow?
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Solution:
Total percentage accounted for:
`32% (blue) + 44% (red) = 76%`
So yellow balls = `100% - 76% = 24%`
Now find 24% of 150:
`0.24 × 150 = 36`
✔ Answer: 36 yellow balls
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3) I toss a coin lots of times. It comes down tails 42% of the time. How many heads did I toss?
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Solution:
This is the
trick/impossible problem.
We’re told the coin lands tails 42% of the time — which implies heads would be `100% - 42% = 58%`.
But we are
not told how many total tosses there were. Without the total number of tosses, we cannot calculate the *actual number* of heads — only the percentage.
✘ Answer: Impossible to determine.
*(We need the total number of tosses to find the number of heads.)*
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4) A piece of hematite contains 72% iron. If the hematite weighed 160g, how much iron would there be?
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Solution:
`0.72 × 160 = 115.2`
✔ Answer: 115.2 grams of iron
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5) In a basketball game, Sally is the top scorer with 45% of the team’s points. If the team scored 120 points in total, how many points did the rest of the team score?
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Solution:
Sally scored: `0.45 × 120 = 54`
Rest of team: `120 - 54 = 66`
✔ Answer: 66 points
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6) A survey of 1250 trees in a small wood showed that 32% were oak trees, 26% were birch trees and the remainder were pine trees. How many pine trees were there?
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Solution:
Oak + Birch = `32% + 26% = 58%`
Pine = `100% - 58% = 42%`
`0.42 × 1250 = 525`
✔ Answer: 525 pine trees
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7) A toy helicopter costs $64 before sales tax. If the sales tax is 5%, how much would it cost to buy?
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Solution:
Tax amount: `0.05 × 64 = 3.20`
Total cost: `64 + 3.20 = 67.20`
✔ Answer: $67.20
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8) In a school survey of 450 pupils, 64% walk to school regularly. How many children is this?
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Solution:
`0.64 × 450 = 288`
✔ Answer: 288 children
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##
✔ Final Answer:
The
impossible/trick problem is #3.
>
“I toss a coin lots of times. It comes down tails 42% of the time. How many heads did I toss?”
You cannot determine the *number* of heads without knowing the *total number of tosses*. You can only say heads occurred 58% of the time — not how many times.
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Let me know if you’d like to see any step explained further!
Parent Tip: Review the logic above to help your child master the concept of percentage word problems worksheet for grade 7.
![Free Printable Proportion Word Problems Worksheets [PDFs]](/images2/percentage-word-problems-worksheet-for-grade-7/percentage-word-problems-worksheet-for-grade-7-25.jpg)
