The table below shows the number of toys collected by Sunshine Centre in Year 2021 and Year 2022. Part of the table is covered by an ink blot. The number of soft toys collected and the total number of toys collected were both three-digit numbers.
Type of ToysYear 2021Year 2022
Wooden Toys12180
Electronic Toys6574
Soft Toys18[blot]200
Total number of toys3[blot][blot]354
Each of the statements is either true, false or not possible to tell from the information given. For each statement, put a tick (✓\checkmark) to indicate your answer.
StatementTrueFalseNot possible to tell
In Year 2021, more than 50% of the toys collected were soft toys.
In Year 2021, 20% of the toys collected were electronic toys.
In Year 2022, the number of wooden toys collected was 40% of the number of soft toys collected.

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Worked solution

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1. Evaluate Statement 1 by setting up an inequality for the number of soft toys in 2021.

Let the number of soft toys in 2021 be SS. The total number of toys is 121+65+S=186+S121 + 65 + S = 186 + S.
For soft toys to be more than 50%50\% of the total:
S>0.5(186+S)S > 0.5(186 + S)
S>93+0.5SS > 93 + 0.5S
0.5S>930.5S > 93
S>186S > 186
Since SS is a 3-digit number starting with '18', SS can be any integer from 180180 to 189189. If S≤186S \le 186, the statement is false. If S>186S > 186, the statement is true. Thus, it is not possible to tell.

2. Evaluate Statement 2 by checking if 65 is 20% of the total toys in 2021.

If 6565 electronic toys were 20%20\% of the total, the total number of toys would be 65÷0.2=32565 \div 0.2 = 325.
However, the minimum possible total is 186+180=366186 + 180 = 366.
Since 366>325366 > 325, the electronic toys cannot be 20%20\% of the total. The statement is False.

3. Evaluate Statement 3 by calculating the percentage of wooden toys relative to soft toys in 2022.

In 2022, there were 8080 wooden toys and 200200 soft toys.
Percentage =80200×100%=40%= \frac{80}{200} \times 100\% = 40\%.
The statement is True.

Answer

Statement 1: Not possible to tell
Statement 2: False
Statement 3: True

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