Solve for Total: Finding Shop Inventory When 30% = Standard Issue Dolls

Percentage Word Problems with Total Finding

If 30% of the dolls in a toy shop are standard issue and the remaining 21 dolls are limited edition. How many dolls are there in the shop in total?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

If 30% of the dolls in a toy shop are standard issue and the remaining 21 dolls are limited edition. How many dolls are there in the shop in total?

2

Step-by-step solution

To solve this problem, follow these steps:

  • Step 1: Define the total number of dolls in the toy shop as x x .
  • Step 2: Note that 30% of these dolls are standard issue, thus 0.30x 0.30x are standard issue dolls.
  • Step 3: Since 70% of the dolls are limited edition (as standard and limited edition must account for 100% of the shop's dolls), 0.70x 0.70x would be limited edition dolls.
  • Step 4: Set up the equation: 0.70x=21 0.70x = 21 , since we know the exact count of limited edition dolls is 21.
  • Step 5: Solve for x x by dividing both sides of the equation by 0.70:
\begin{align*} 0.70x &= 21 \\ x &= \frac{21}{0.70} \\ x &= 30 \end{align*}

Therefore, the total number of dolls in the shop is 30 30 .

3

Final Answer

30

Key Points to Remember

Essential concepts to master this topic
  • Rule: If 30% are standard, then 70% are limited edition
  • Technique: Set up equation 0.70x = 21, then divide by 0.70
  • Check: Verify 30% of 30 = 9 standard, plus 21 limited = 30 total ✓

Common Mistakes

Avoid these frequent errors
  • Setting up equation with the 30% instead of 70%
    Don't write 0.30x = 21 because 30% are standard issue dolls = wrong portion! This gives x = 70 which is incorrect. Always identify which percentage matches the given quantity - here 21 dolls are the remaining 70%.

Practice Quiz

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Solve for X:

\( 3x=18 \)

FAQ

Everything you need to know about this question

Why can't I just use the 30% in my equation?

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Because we know the count of limited edition dolls (21), not standard issue dolls! The 30% represents standard dolls, but we need to use the percentage that matches our known quantity.

How do I know which percentage to use in the equation?

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Always match the given number with its corresponding percentage. Since 21 dolls are limited edition, and limited edition = 100% - 30% = 70%, use 0.70x = 21.

What if the problem gave me the number of standard dolls instead?

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Then you'd use the 30%! If 9 dolls were standard issue, your equation would be 0.30x = 9, giving the same answer of x = 30 total dolls.

Can I solve this without using decimals?

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Yes! You can write 70100x=21 \frac{70}{100}x = 21 or even 710x=21 \frac{7}{10}x = 21 . Then multiply both sides by the reciprocal to solve.

How do I check my answer is correct?

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Calculate both parts: 30% of 30 = 9 standard dolls and 70% of 30 = 21 limited dolls. Since 9 + 21 = 30 total, your answer checks out!

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